tag:blogger.com,1999:blog-6117566427377805302024-03-13T22:33:41.181-07:00Math 3 Teachers GuideSTEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-611756642737780530.post-37699230772392969992011-03-23T18:46:00.000-07:002011-03-23T18:46:41.925-07:00Summative Test<div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>12.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="0" width="50"></td></tr>
<tr><td></td><td><br />
</td></tr>
</tbody></table><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br clear="ALL" /></span><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></span><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</span><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, </span><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>are adjacent angles. If </span><span style="font-family: Cambria, serif; font-size: 10pt;">, what is </span><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>in degrees?</span><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">12<span> </span>c. 96</span><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">24<span> </span>d. 100</span><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>13.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The measure of an angle is 14 less than thrice the measure of its complement. The measure of the angle is <u><span> </span></u>.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">26<span> </span>c. 64<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">52<span> </span>d. 78<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>14.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">If two angles are both congruent and supplementary, then each is <u><span> </span></u>.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">An acute angle<span> </span>c. obtuse angle<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">A right angle<span> </span>d. exterior angle<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>15.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;"><A and < B are supplementary. If m<A = 2x – 30 and m<B = x + 60, what is m<A?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span></span></div><table cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="0" width="21"></td></tr>
<tr><td></td><td><br />
</td></tr>
</tbody></table><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br clear="ALL" /></span><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Cambria, serif; font-size: 10pt;">50<span> </span>c.<span> </span>110<o:p></o:p></span></span><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</span><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">70<span> </span>d.<span> </span>60<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>16.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, </span><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>intersect at <i>B</i>. What is m<<i>ABE</i>?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">130<span> </span>c. 48<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">60<span> </span>d. 44<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>17.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;"><A and <B are congruent angles. If <i>m<A = 10x – 20 and m<B = 8x +2, then <A is<u><span> </span></u></i>.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Acute angle<span> </span>c. obtuse angle<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Right triangle<span> </span>d. cannot be determined<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>18.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">If the measures of <i><ABE, < EBD, and <DBC </i>are in the ratio. 2:4:6, respectively, what is <i>m<DBC?</i><o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">15<span> </span>c. 60<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">30<span> </span><span> </span>d. 90<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>19.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The measure of the supplement of an angle is 12 more than twice the measure of the angle. What is the measure of the angle?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">124<span> </span>c. 48<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">56<span> </span>d. 24<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>20.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">What is the measure of the angle if twice the measure of its complement is 35 less than its supplement?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">35<span> </span>c. 70<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">45<span> </span>d. 75<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>21.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">If two angles form a linear pair and the measure of one of them is 64, what is the measure of the other?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">26<span> </span>c. 116<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">64<span> </span>d. 296<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>22.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">They are nonadjacent angles formed by two intersecting lines.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Supplementary angles<span> </span>c. complementary angles<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Linear pairs<span> </span>d. vertical angles<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>23.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">How large is the angle made by the hands of a clock at 4:15?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">30<span> </span>c. 60<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">37.5<span> </span>d. 60.5<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>24.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Which segments of the given lengths cannot be the side of a triangle?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">9 cm, 8 cm, 3 cm<span> </span>c. 9 cm, 6 cm, 3 cm<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">5 cm, 4 cm, 2 cm<span> </span>d. 11 cm, 12 cm, 13 cm<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>25.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above triangle, <i>AC = 13 cm </i>and <i>AB = 17 cm</i>. What is the range of values of<i>segment BC</i>?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">13 cm <<i>BC</i> < 17 cm<span> </span>c. 4 cm <<i>BC</i> < 17 cm<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">13 cm <<i>BC</i> < 30 cm<span> </span>d. 4 cm <<i>BC</i> < 30 cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>26.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The value of <i>x</i> that will make <i>l<sub>1</sub></i> parallel to <i>l<sub>2</sub> </i>is <u><span> </span></u><span> </span>.<i><o:p></o:p></i></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">8<span> </span>c. 14<i><o:p></o:p></i></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">11<span> </span>d. 17<i><o:p></o:p></i></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>27.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">What is the possible range of <i>AC</i> in the above figure?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">3 < <i>AC</i> <32<span> </span>c. 3 < <i>AC</i> <31<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">8 < <i>AC</i> <32<span> </span>d. 8 < <i>AC</i> <31<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>28.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">What is <i>x </i>equal to in the above figure?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">70°<span> </span>c. 50°<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">60°<span> </span>d. 30°<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>29.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, <i>ray OA is perpendicular to ray OC and ray OB is perpendicular to OD</i>. If <i>m<BOC = 30, </i>what is the sum of the measures of<i><u> </u><AOB and <DOC</i>?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">30<span> </span>c. 60<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">120<span> </span>d. cannot be determined<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>30.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, <i>ray AB is perpendicular to ray AC</i>. If <i>m<EAD = 2m<DAC and m<BAE = 3m<DAC, </i>what is <i>m< DAC</i>?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">15<span> </span>c. 45<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">30<span> </span>d. 90<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">B. Proving</span></b><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Write a two-column proof.<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Given: <i>segment AC parallel to segment ED</i><o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><i><span style="font-family: Cambria, serif; font-size: 10pt;"><A congruent to <C<o:p></o:p></span></i></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>Prove: <i><A is congruent to <EDB<o:p></o:p></i></span></div><div class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span class="Apple-style-span" style="font-family: Cambria, serif;"><br />
</span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Given: <i>ray BD perpendicular to ray BA</i><o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><i><span style="font-family: Cambria, serif; font-size: 10pt;">ray Be perpendicular to ray BC<o:p></o:p></span></i></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>Prove: <i><ABD is congruent to <CBE<o:p></o:p></i></span></div><div class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span class="Apple-style-span" style="font-family: Cambria, serif;"><i><br />
</i></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span style="font-family: Cambria, serif; font-size: 10pt;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span><b>Assignment</b><o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Answer the problem For Math<i>itiniks</i> on page 200 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">Summative Test 3<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><i><span style="font-family: Cambria, serif; font-size: 10pt;">Triangle Congruence<o:p></o:p></span></i></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><span style="font-family: Cambria, serif; font-size: 10pt;">(1 session)<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">I. Target Proficiency<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span></span></b><span style="font-family: Cambria, serif; font-size: 10pt;">At least 75% of the students be able to get at least 75% correct items in the test.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">II. Procedure<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Administer the test.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Clarify the directions and announce any corrections made in the test paper.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Inculcate the importance of honesty. Encourage them to do their best.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">III. Questionnaire<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Multiple Choice<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Write the letter of the correct answer on the blank before each number.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 1. Which of the following correspondence is equivalent to <i>CAT↔ DOG</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>a. TCA ↔ DGO<span> </span>b. CTA ↔ DGO<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>c. ATC ↔ ODG<span> </span>d. TAC ↔ OGD<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 2. </span><span style="font-family: Cambria, serif; font-size: 10pt;">In the figure, <i>ray BD </i>bisects <i><ABC</i>. If <i>m<CBD =36</i>, what is <i>m<ABC</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 135pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">72<span> </span>b. 63<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 135pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">36<span> </span>d. 18<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 3. The bisectors of two supplementary adjacent angles form an angle with the measure of ______.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 135pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">45<span> </span>c. 90<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 135pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">60<span> </span>d. 180<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 4. <i>ray DF </i>bisects <i>< CDE</i>. If <i>m<CDF= 2x +10 </i>and <i>m<EDF= 4x – 10</i>, what is <i>m<CDE</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">10<span> </span>c. 30<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">20<span> </span>d. 60<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 5. What is <i>x </i>in the figure?</span><span style="font-family: Cambria, serif; font-size: 10pt;"> </span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">40<span> </span>c. 70<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">60 <span> </span>d. 80<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 6. If the bisector of an angle of a triangle is perpendicular to the opposite side, then the triangle is <u><span> </span></u>.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Acute<span> </span>c. obtuse<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Isosceles<span> </span>d. right triangle<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 7. In triangle <i>ABC</i>, <i><B is congruent to <C</i>. If <i>AB=2x + 4 </i>and <i>AC=5x – 8, </i>then <i>AB =<span> </span>_______</i>.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Acute<span> </span>c. isosceles<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">obtuse <span> </span>d. right triangle<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 8. In triangle <i>CDE</i>, <i>segment CD congruent to ED</i>. If <i>m<C=3x+10 </i>and <i>m<E=5x-30</i>, what is <i>m<D</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">80<span> </span>c. 50<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">70<span> </span>d. 40<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 9. <i>Triangle EFG </i>is an isosceles triangle with segment EG congruent to segment FG and m<F = 75. What is m<G?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">30<span> </span>c. 50<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">40<span> </span>d. 60<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 10. In triangle ABC, <C is a right angle. If m<A = 2x+40 and m<B = 4x – 10, what is m<B?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">30<span> </span>c. 50<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">40<span> </span>d. 60<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 11. Triangle SAR is an isosceles triangle with <A congruent to <R. if SA= 8x – 40 and SR=5x+20, what is SA+SR?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">20<span> </span>c. 120<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">40<span> </span>d. 240<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 12. </span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">In the figure, CD is perpendicular bisector of segment AB. E lies on CD. If AE= ½ x+7 and BE=2/3 x+6, what is x?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">4<span> </span>c. 8<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">5<span> </span>d. 7<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____13. </span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">In the figure, PA=QA, PB=QB and R lies on AB. If PR=4(20-x) and QE= 6(x+5), what is 3x?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">5<span> </span>c. 15<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">10<span> </span>d. 20<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____ 14. </span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">In the figure, if line ES is the perpendicular bisector of segment BT and BT= 8 and BE=6, what is line ES?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 17px; position: relative; top: 16.5pt;"><img height="36" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image040.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1025" width="24" /></span><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>c. </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 17px; position: relative; top: 16.5pt;"><img height="36" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image042.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1025" width="24" /></span><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 17px; position: relative; top: 16.5pt;"><img height="36" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image044.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1025" width="24" /></span><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>d. </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 17px; position: relative; top: 16.5pt;"><img height="34" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image046.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1025" width="15" /></span><span style="font-family: Cambria, serif; font-size: 10pt;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____15. </span><span style="font-family: Cambria, serif; font-size: 10pt;">Name the sides of the triangle above in order of increasing length.<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">AB, BC, AC<span> </span>c. AB, AC, BC<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">AC, BC, AB<span> </span>d. BC, AC, AB<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Proving<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Complete the proof of the following.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Given: <1 congruent to <2<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>Ray AD bisects angle BAC<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Prove: ray AD is the perpendicular bisector of segment BC<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: justify;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Proof:<o:p></o:p></span></div><table border="0" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><tbody>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div align="center" class="MsoListParagraphCxSpMiddle" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><span style="font-family: Cambria, serif; font-size: 10pt;">Statements<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div align="center" class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in; text-align: center; text-indent: -0.5in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Reasons<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoNormal" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">1.___________________________________________________<u><o:p></o:p></u></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoNormal" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">1.Given<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">2.___________________________________________________<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>____________________________________________________<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">2. Vertical angles are congruent<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">3.<ABD congruent to <ACD<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">3. _________________________________________________<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">4.segment AB congruent to segment AC<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">4._________________________________________________<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">5.ray AD bisects <BAC<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">5.__________________________________________________<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">6.__________________________________________________<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">6. Definition of Angle Bisector<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">7.triangle ABD congruent to ACD<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">7.__________________________________________________<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">8.segment DB congruent to DC<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">8.__________________________________________________<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">9.___________________________________________________<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>____________________________________________________<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">9.Definition of Congruent Segments<o:p></o:p></span></div></td></tr>
<tr><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.3pt;" valign="top" width="284"><div class="MsoListParagraphCxSpFirst" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">10. line AD is the perpendicular bisector of segment BC<o:p></o:p></span></div></td><td style="padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 211.5pt;" valign="top" width="282"><div class="MsoListParagraphCxSpLast" style="margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">10._________________________________________________<o:p></o:p></span></div></td></tr>
</tbody></table><div class="MsoListParagraph" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">Summative Test 4<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span style="font-family: Cambria, serif; font-size: 10pt;">Quadrilaterals<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><span style="font-family: Cambria, serif; font-size: 10pt;">(1 session)<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Target Proficiency<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">At least 75% of the students should be able to get at least 75% correct items in the test.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Procedure<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Check the test.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Administer the test.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Clarify the directions and announce any corrections made in the test paper.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Inculcate the importance of honesty. Encourage them to do their best.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Questionnaire<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Multiple Choice<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">Write the letter of the correct answer in the blank before each number.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____1. It is the quadrilateral with exactly one pair of parallel sides.<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Rectangle<span> </span>c. square<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Rhombus<span> </span>d. trapezoid<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____2. </span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, if AD = 6(x-3)+8 and BC=2(7-x), what is AD+BC?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">12<span> </span>c. 16<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">14<span> </span>d. 18<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____3. In the number 2 figure, if DC=4x-10, AB=14,AD=x+2y, and BC=12, what is y?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">4<span> </span>c. 2<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">3<span> </span>d. 1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____4. </span><span style="font-family: Cambria, serif; font-size: 10pt;">Quadrilateral ABCD is a parallelogram. Find x and y if AE=x+3y, CE=6, DE= 2x-3y, and BE=3.<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">x=1, y=3<span> </span>c. x=2, y=3<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">x=3, y=1<span> </span>d. x=3, y=2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____5. ABCD is a parallelogram. Its diagonals AC and BC intersect at E. if DE=4x+8 and BE=6x-26, what is BD?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">17<span> </span>c. 76<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">34<span> </span>d. 152<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____6. ABCD is a rectangle. If diagonal AC=4x+5 and diagonal BD=6x-1, what is AC+BD?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">17<span> </span>c. 43<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">34<span> </span>d. 21<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____7.</span><span style="font-family: Cambria, serif; font-size: 10pt;"> </span><span style="font-family: Cambria, serif; font-size: 10pt;"><span> </span>MATH is a rhombus. If m<H=2(4x+40) and m<A=3(30+2x), what is m<M?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">120<span> </span>c. 5<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">60<span> </span>d. 10<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____8. </span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, D and B are midpoints of EC and AC respectively. If BD=1, what is BD+AE?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">6<span> </span>c. 36<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">24<span> </span>d. 72<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____9. Which of the following statements is false?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The diagonals of a rectangle are congruent<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The diagonals of a square bisect the vertex angle<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The diagonals of a rhombus are perpendicular<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">The diagonals of a parallelogram are congruent<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____10. </span><span style="font-family: Cambria, serif; font-size: 10pt;">In the figure above, D and E are midpoints of AB and BC, respectively. If m<A=55 and m<B=32, what is m<DEB?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">90<span> </span>c. 92<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">91<span> </span>d. 93<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____11. </span><span style="font-family: Cambria, serif; font-size: 10pt;">Quadrilateral ABCD is a rectangle. If m<CAB=25, what is m<DBC?<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">25<span> </span>c. 65<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">50<span> </span>d. 75<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____12. One angle of an isosceles trapezoid has a measure of 50. The measures of the other angles are.<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">50, 50, 130<span> </span>c. 50, 130, 130<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">50, 50, 50<span> </span>d. 130, 130, 130<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____13. An isosceles trapezoid has sides of lengths 5, 8, 5, and 14. The lenghth of its median is ________.<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">11<span> </span>c. 16<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">22<span> </span>d. 32<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____14. Which of the following is false?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Every square is a rectangle.<span> </span>c. Every square is a parallelogram.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">Every square is a rhombus<span> </span>d. Every rhombus is a square.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____15. </span><span style="font-family: Cambria, serif; font-size: 10pt;">In the above figure, D and E are midpoints of AB and AC, respectively. If DE =3x+4 and BC = 8x-20, what is BC?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">14<span> </span>c. 66<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">46<span> </span>d. 92<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____16. ABCD is an isosceles trapezoid where AB congruent to DC. If m<A=2(x+20) and m<D=6x -20, what is m<C?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">15<span> </span>c. 110<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">70<span> </span>d. 130<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">_____17. </span><span style="font-family: Cambria, serif; font-size: 10pt;">A trapezoid and its median are shown above the figure. Find the value of x.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">12<span> </span>c. 10<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">11<span> </span>d. 9<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Cambria, serif; font-size: 10pt;">______18. ABCD is an isosceles trapezoid with AD congruent BC. If m<DAB=(2(x-10) and m<ADC=4x-40, what is m<B?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">40<span> </span>c. 100<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Cambria, serif; font-size: 10pt;">60<span> </span>d. 120</span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Cambria, serif; font-size: 10pt;"></span></div><div class="Section1" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><div class="MsoNormal"><span style="font-family: Calibri, sans-serif;">____ 19. What is the area of a kite with diagonals 10 dm and 16 dm?<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">160<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">80<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">52<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="height: 160px; left: 0px; margin-left: 36px; margin-top: 6px; position: absolute; width: 169px; z-index: -24;"><img height="160" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1026" width="169" /></span><span style="font-family: Calibri, sans-serif;">26<o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: Calibri, sans-serif;">____ 20.<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 2in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">In Triangle ABC, X, Y, Z are the midpoints of sides AC, AB and BC respectively. If the perimeter of triangle ABC is 108 cm, then the perimeter of triangle XYZ is<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 2in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="margin-left: 2in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">72<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">54<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">36<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">27<o:p></o:p></span></div><div class="MsoNormal"><span style="height: 171px; margin-left: 348px; margin-top: 11px; position: absolute; width: 180px; z-index: -23;"><img height="171" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1027" width="180" /></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: Calibri, sans-serif;">B. Proving<o:p></o:p></span></div><div class="MsoNormal" style="text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">1. Complete the Proof of the following:<o:p></o:p></span></div><div class="MsoNormal" style="text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">Given: Triangle BEC is an isosceles triangle<o:p></o:p></span></div><div class="MsoNormal" style="margin-left: 0.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">ABCD is a rectangle<o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: Calibri, sans-serif;"><span> </span>Prove: E is the midpoint of AD<o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: Calibri, sans-serif;"><span> </span><o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: Calibri, sans-serif;">Proof:<o:p></o:p></span></div></div><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif; font-size: 12pt;"><br clear="all" style="page-break-before: auto;" /></span></span><div class="Section2" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: Calibri, sans-serif;">Statements<o:p></o:p></span></div><div class="MsoNormal"><br />
</div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Triangle BEC is an isosceles triangle<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">BE is congruent to CE<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">ABCD is a rectangle<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">AB is congruent to DC<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Angle A and Angle E are right angles<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Triangle BAE and triangle CDE are right triangles<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Triangle BAE is congruent to triangle CDE<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">AE is congruent to DE<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">E is the midpoint of AD<o:p></o:p></span></li>
</ol><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: Calibri, sans-serif;">Reasons<o:p></o:p></span></div><div class="MsoNormal"><br />
</div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
</ol><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><ol start="2" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
</ol><div class="MsoNormal" style="margin-left: 0.25in;"><br />
</div><ol start="6" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
</ol><div class="MsoNormal"><br />
</div><ol start="7" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
</ol><div class="MsoNormal"><br />
</div><ol start="8" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="height: 142px; left: 0px; margin-left: 36px; margin-top: 38px; position: absolute; width: 216px; z-index: -22;"><img height="142" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1028" width="216" /></span><span style="font-family: Calibri, sans-serif;">____________________<o:p></o:p></span></li>
</ol></div><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif; font-size: 12pt;"><br clear="all" style="page-break-before: auto;" /></span></span><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri, sans-serif;">2. Write a two-column proof<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri, sans-serif;"><span> </span>Given: Angle 1 is congruent to angle 2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri, sans-serif;"><span> </span>AD is congruent to BC<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri, sans-serif;">Prove: Quadrilateral ABCD is a parallelogram<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">IV. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">Answer the problem for Mathitiniks on page 346 of the textbook<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center; text-indent: 0.5in;"><b><span style="font-family: Calibri, sans-serif;">Summative Test 5<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center; text-indent: 0.5in;"><b><span style="font-family: Calibri, sans-serif;">Similarity<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-family: Calibri, sans-serif;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Target Proficiency<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Calibri, sans-serif;"><span> </span></span></b><span style="font-family: Calibri, sans-serif;">At least 75% of the students should be able to get 75% correct items in the test.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-family: Calibri, sans-serif;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Procedure<o:p></o:p></span></b></div><ol start="1" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Check the Assignment<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Administer the test.<o:p></o:p></span></li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Clarify the directions and announce any corrections made in the test paper<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;"><span> </span>Inculcate the importance of honesty. Encourage them to do their best<span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-family: Calibri, sans-serif;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Questionnaire<o:p></o:p></span></b></div><ol start="1" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><b><span style="font-family: Calibri, sans-serif;">Multiple Choice<o:p></o:p></span></b></li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><b><span style="font-family: Calibri, sans-serif;"><span> </span></span></b><span style="font-family: Calibri, sans-serif;">Write the letter of the correct answer on the blank before each number<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____1. The ratio of the measure of one angle of an equiangular triangle to the sum<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>of the interior angles of a pentagon is _____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 1: 6<span> </span>b. 1:9<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 2: 6<span> </span><span> </span>d. 2:9<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____2. The ratio of female students to male students in a certain school is 5 : 4. If there are 850 female students, what is the total students population of the school?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 680<span> </span><span> </span>b. 750<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 1 530<span> </span>d. 1600<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____3. The geometric mean of 16 and 9 is _____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 25<span> </span>b. 12<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 8<span> </span><span> </span>d. 7<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____4. An angle is 10 more that its complement. The ratio of the angle to its complement is _____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 123px; margin-left: 48px; margin-top: 17px; position: absolute; width: 216px; z-index: -21;"><img height="123" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1029" width="216" /></span><span style="font-family: Calibri, sans-serif;"><span> </span>a. 5:4<span> </span>b. 4:5<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 4:9 <span> </span>d.5:9<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____5.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">In the above figure, <i>DE</i> ǁ <i>BC</i>. Find x.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 3<span> </span>b. 4<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 5<span> </span><span> </span>d. 6<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="position: relative; z-index: -20;"><span style="height: 127px; left: 48px; position: absolute; top: -12px; width: 232px;"><img height="127" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image010.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1030" width="232" /></span></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____6.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">In the above figure, </span><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">B</span></i><span style="font-family: Calibri, sans-serif;"> </span><span style="font-family: 'Adobe Fangsong Std R', serif;">≌∠</span><i><span style="font-family: Calibri, sans-serif;">DEA</span></i><span style="font-family: Calibri, sans-serif;">. If <i>AE</i> =6, <i>AB</i>=9, and <i>AD</i>=8. What is DC?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 4<span> </span>b. 3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 2<span> </span><span> </span>d. 1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 133px; margin-left: 60px; margin-top: 17px; position: absolute; width: 360px; z-index: -19;"><img height="133" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image012.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1031" width="360" /></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____7.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">Δ<i>ABC</i> </span><span style="font-family: Calibri, sans-serif;"><span> </span></span><span style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">∼</span><span style="font-family: Calibri, sans-serif;">Δ<i>DEF</i>. If<i> a</i>=6, <i>b</i>=4, <i>c</i>=10, and <i>d</i>=8, what is <i>e</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 5 1/3<span> </span>b. 6<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 165px; margin-left: 60px; margin-top: 7px; position: absolute; width: 240px; z-index: -18;"><img height="165" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image014.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1032" width="240" /></span><span style="font-family: Calibri, sans-serif;"><span> </span>c. 6 1/3<span> </span><span> </span><span> </span>d. 7<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____8.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>In the above figure, <i>AE</i>=15, <i>BC</i>=6, and <i>CD</i>=3. What is <i>CE</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. </span><span lang="FIL-PH"><span> </span>3<span> </span></span><span style="font-family: Calibri, sans-serif;">b. 5</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c.<span> </span>9<span> </span>d. 21</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 150px; margin-left: 60px; margin-top: 7px; position: absolute; width: 264px; z-index: -17;"><img height="150" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image016.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1033" width="264" /></span><span style="font-family: Calibri, sans-serif;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____9.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">ΔABC is a right triangle with altitude <i>CD</i>. If<i> AD</i>=5, <i>DB</i>=7, what is<i> AC</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 60</span><span lang="FIL-PH" style="font-family: Calibri, sans-serif;"><span> </span></span><span style="font-family: Calibri, sans-serif;">b. 35</span><span lang="FIL-PH" style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c.15√2</span><span lang="FIL-PH" style="font-family: Calibri, sans-serif;"><span> </span></span><span style="font-family: Calibri, sans-serif;"><span> </span>d. 2√15</span><span lang="FIL-PH" style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="position: relative; z-index: -16;"><span style="height: 153px; left: 24px; position: absolute; top: -48px; width: 216px;"><img height="153" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image018.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1034" width="216" /></span></span><span style="font-family: Calibri, sans-serif;">_____10.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">In the above figure<i>,<span> </span>AC</i> <span> </span></span><span lang="FIL-PH" style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">⊥</span><i><span style="font-family: Calibri, sans-serif;">AB</span></i><span style="font-family: Calibri, sans-serif;"> and <i>AD</i> </span><span style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">⊥</span><i><span style="font-family: Calibri, sans-serif;">BC</span></i><span style="font-family: Calibri, sans-serif;">. If<i> BC</i>=20, what is<i> DB</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 50<span> </span>b. 40<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 10 <span> </span>d. 5<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____11. The areas of two similar triangles are equal to36 cm<sup>2</sup> and<span> </span>81 cm<sup>2</sup>. what is the ratio of a pair of corresponding sides.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 6:9<span> </span>b. 2:3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 3:6<span> </span>d. 8:1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____12. The corresponding medians of two similar triangles are 3 cm<span> </span>and 7 cm, respectively. The ratio of their areas is ___.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 6:14<span> </span>b. 9:49<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 9:27<span> </span>d. 4:10<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____13. The areas of two similar triangles are 81 cm<sup> 2</sup> and 121 cm <sup>2</sup>, respectively. The ratio of the corresponding altitudes is____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a.81:121<span> </span>b. 8:1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c.9:11<span> </span>d. 1:21<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____14. The ratio of pair of corresponding<span> </span>sides of two similar triangles is 5 : 3. The ratio of their perimeters is____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 25:9<span> </span>b. 5:3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 5:8<span> </span>d. 8:3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____15. The ratio of the areas of two similar triangles is<u> 4. </u><span> </span>The ratio of a pair of<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span><span> </span>81<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a corresponding angle bisectors is____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 4:81<span> </span>b. 81:4<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 129px; margin-left: 60px; margin-top: 6px; position: absolute; width: 288px; z-index: -15;"><img height="129" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image020.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1035" width="288" /></span><span style="font-family: Calibri, sans-serif;">c. 2:9<span> </span>d. 4:9<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____16.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">In the above figure, <i>CD</i> <span> </span>bisects </span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">ACB</span></i><span style="font-family: Calibri, sans-serif;">. If<i> AB</i> =16, <i>AC</i>=8 and <i>BC</i>=12, what is<i> AD</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 4<span> </span>b. 6.4<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 8<span> </span>d. 9.6<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 121px; margin-left: 60px; margin-top: 0px; position: absolute; width: 228px; z-index: -14;"><img height="121" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image022.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1036" width="228" /></span><span lang="FIL-PH" style="font-family: Calibri, sans-serif;"><span> </span></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____17.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">In Δ<i>ABC</i> above<i> AC</i>=10 cm<i>, BC</i>=10 cm, m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">A</span></i><span style="font-family: Calibri, sans-serif;">=30, and m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">B</span></i><span style="font-family: Calibri, sans-serif;">=30. What is <i>AB</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 3√5cm<span> </span>b. 5√3cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 159px; margin-left: 60px; margin-top: 17px; position: absolute; width: 384px; z-index: -13;"><img height="159" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image024.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1037" width="384" /></span><span style="font-family: Calibri, sans-serif;">b. 3√10 <span> </span>d. 10√3cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____18.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">Δ<i>ABC</i> </span><span lang="FIL-PH" style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">∼</span><span style="font-family: Calibri, sans-serif;">Δ<i>DEF</i>. The perimeter of Δ<i>DEF</i> is ____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 9 cm <span> </span>b. 14cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 217px; margin-left: 60px; margin-top: 12px; position: absolute; width: 288px; z-index: -12;"><img height="217" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image026.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1038" width="288" /></span><span style="font-family: Calibri, sans-serif;">c. 24 cm<span> </span>d. 28 cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____19.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">In the above figure,<i> a</i>ǁ<i>b</i>ǁ<i>c</i>. what is <i>x</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 5 5/7 <span> </span>b.6<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 143px; margin-left: 60px; margin-top: 10px; position: absolute; width: 264px; z-index: -11;"><img height="143" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image028.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1039" width="264" /></span><span style="font-family: Calibri, sans-serif;">c. 6 5/7<span> </span>d. 7<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____20.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">Triangle <i>ABC</i> is a right triangle with altitude<i> CD</i>. If <i>AD</i>=25 cm and <i>BD</i>=36 cm, what is the area of Δ<i>ABC</i>?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 915 cm<sup> 2</sup><span> </span>b. 900 cm<sup> 2</sup><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 450 cm<sup> 2</sup><span> </span>d. 61 cm<sup> 2</sup><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 170px; margin-left: 312px; margin-top: 12px; position: absolute; width: 276px; z-index: -10;"><img height="170" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image030.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1040" width="276" /></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">B. Proving<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Complete the proof of the following:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 29.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Given: Quadrilateral<i> ABCD</i> is a rectangle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>__<span> </span>__<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>AE ǁ FG<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Prove: ΔDAE </span><span lang="FIL-PH" style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">∼</span><span style="font-family: Calibri, sans-serif;">ΔBGF<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><i><span style="font-family: Calibri, sans-serif;">Proof:<o:p></o:p></span></i></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td style="border-bottom-color: windowtext; border-bottom-style: solid; border-bottom-width: 1pt; border-left-color: windowtext; border-left-style: solid; border-left-width: 1pt; border-right-color: windowtext; border-right-style: solid; border-right-width: 1pt; border-top-color: windowtext; border-top-style: solid; border-top-width: 1pt; padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.05pt;" valign="top" width="284"><div align="center" class="MsoNormal" style="text-align: center;"><b><i><span style="font-family: Calibri, sans-serif;">Statements<o:p></o:p></span></i></b></div></td><td style="border-bottom-color: windowtext; border-bottom-style: solid; border-bottom-width: 1pt; border-left-color: windowtext; border-left-style: solid; border-left-width: 1pt; border-right-color: windowtext; border-right-style: solid; border-right-width: 1pt; border-top-color: windowtext; border-top-style: solid; border-top-width: 1pt; padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.05pt;" valign="top" width="284"><div align="center" class="MsoNormal" style="text-align: center;"><b><i><span style="font-family: Calibri, sans-serif;">Reasons<o:p></o:p></span></i></b></div></td></tr>
<tr><td style="border-bottom-color: windowtext; border-bottom-style: solid; border-bottom-width: 1pt; border-left-color: windowtext; border-left-style: solid; border-left-width: 1pt; border-right-color: windowtext; border-right-style: solid; border-right-width: 1pt; border-top-color: windowtext; border-top-style: solid; border-top-width: 1pt; padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.05pt;" valign="top" width="284"><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Quadrilateral <i>ABCD </i>is rectangle.<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">D</span></i><span style="font-family: Calibri, sans-serif;"> and </span><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">B</span></i><span style="font-family: Calibri, sans-serif;"><span> </span>are right angles.<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">D</span></i><span style="font-family: Calibri, sans-serif;"> </span><span style="font-family: 'Adobe Fangsong Std R', serif;">≌∠</span><i><span style="font-family: Calibri, sans-serif;">B</span></i><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></li>
</ol><div class="MsoNormal" style="margin-left: 0.5in;"><span style="font-family: Calibri, sans-serif;">__<span> </span>__<o:p></o:p></span></div><ol start="4" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><i><u><span style="font-family: Calibri, sans-serif;">DC</span></u></i><span style="font-family: Calibri, sans-serif;"><span> </span>ǁ<span> </span><i><u>AB</u></i><u><span> </span><o:p></o:p></u></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><i><u><span style="font-family: Calibri, sans-serif;">AE</span></u></i><span style="font-family: Calibri, sans-serif;"><span> </span>ǁ <i><span> </span><u>FG</u></i><u><o:p></o:p></u></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">EAB </span></i><span style="font-family: 'Adobe Fangsong Std R', serif;">≌∠</span><i><span style="font-family: Calibri, sans-serif;">GFB</span></i><u><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></u></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">DEA</span></i><span style="font-family: Calibri, sans-serif;"> </span><span style="font-family: 'Adobe Fangsong Std R', serif;">≌∠</span><i><span style="font-family: Calibri, sans-serif;">EAB</span></i><u><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></u></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><i><span style="font-family: Calibri, sans-serif;">DEA</span></i><span style="font-family: Calibri, sans-serif;"> </span><span style="font-family: 'Adobe Fangsong Std R', serif;">≌∠</span><i><span style="font-family: Calibri, sans-serif;">GFB</span></i><u><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></u></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Δ<i>DAE</i> </span><span style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">∼</span><span style="font-family: Calibri, sans-serif;">Δ<i>BGF</i></span><u><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></u></li>
</ol><div class="MsoNormal"><br />
</div></td><td style="border-bottom-color: windowtext; border-bottom-style: solid; border-bottom-width: 1pt; border-left-color: initial; border-left-style: none; border-left-width: initial; border-right-color: windowtext; border-right-style: solid; border-right-width: 1pt; border-top-color: initial; border-top-style: none; border-top-width: initial; padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 213.05pt;" valign="top" width="284"><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
</ol><div class="MsoNormal"><br />
</div><div class="MsoNormal"><br />
</div><ol start="4" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">________________<o:p></o:p></span></li>
</ol></td></tr>
</tbody></table><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 29.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Write a two-column proof.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>__<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 29.25pt;"><span style="font-family: Calibri, sans-serif;">Given: Quadrilateral <i>ABCD</i> is parallelogram with diagonal <i>AC</i>.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 29.25pt;"><span style="font-family: Calibri, sans-serif;">Prove: Δ<i>ABE</i></span><span lang="FIL-PH" style="font-family: 'Adobe Fan Heiti Std B', sans-serif;">∼</span><span style="font-family: Calibri, sans-serif;"> Δ<i>CDE</i></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-family: Calibri, sans-serif;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Assignment<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Answer the problem For Math<i>itinikins</i> on page 411 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Calibri, sans-serif;">Summative Test 6<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Calibri, sans-serif;">Circles<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span style="font-family: Calibri, sans-serif;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Target Proficiency<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>At least<span> </span>75% of the students should be able to get at least 75% correct items in the test.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span style="font-family: Calibri, sans-serif;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Procedure<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Administer the test<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Clarify the directions and announce any corrections made in the test paper.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Inculcate the importance of honesty. Encourage themto do their best.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span style="font-family: Calibri, sans-serif;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Questionnaire<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span style="font-family: Calibri, sans-serif;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Multiple Choice<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Calibri, sans-serif;">Write the letter of the correct answer in the blank.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____1. It is a line that intersects the circle in two points.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. secant<span> </span>b. tangent<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. diameter<span> </span>d. segment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____2. P is a point in the exterior of a circle. How many tangents to the circle contain P?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 171px; margin-left: 72px; margin-top: 17px; position: absolute; width: 204px; z-index: -8;"><img height="171" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image034.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1042" width="204" /></span><span style="font-family: Calibri, sans-serif;">a. 1<span> </span>b. 2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 3<span> </span>d. 4<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____3.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">Circles A, B, C and above are tangent to each other. If AB=10cm, AC=11 cm, and BC=13, what is the radius of circle A?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 4<span> </span>b.5<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 6<span> </span>d. 7<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="position: relative; z-index: -7;"><span style="height: 176px; left: 72px; position: absolute; top: -12px; width: 192px;"><img height="176" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image036.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1043" width="192" /></span></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____4.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.75in;"><span style="font-family: Calibri, sans-serif;"><span> </span>If diameter AB of circle O is 24 cm long, and m </span><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">ABC=30 <sup>o</sup>, how far chord<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">__<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">BC from the center O.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 30cm<span> </span>b. 24cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 12cm<span> </span>d. 6cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 221px; margin-left: 48px; margin-top: 2px; position: absolute; width: 276px; z-index: -6;"><img height="221" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image038.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1044" width="276" /></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">_____5,<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 3.5in;"><span style="font-family: Calibri, sans-serif;">In the figure, diameters AB and CD intersect at center O of the<span> </span>circle, mA͡C=x, and mC͡B=4x-20. What is m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">AOD in degrees?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 40 <span> </span>b.80<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 120<span> </span>d. 140<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 193px; margin-left: 60px; margin-top: 1px; position: absolute; width: 216px; z-index: -5;"><img height="193" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image040.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1045" width="216" /></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">______6.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.75in;"><span style="font-family: Calibri, sans-serif;"><span> </span>In circle O above, m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">OAB=40<sup> o</sup> , what is the measure of are A͡CB?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>a. 260<span> </span>b. 220<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>c. 100<span> </span>d. 80<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">______7. The central angle of a circle measures 86<sup> o</sup>. The measure of the major are<span> </span>arc of the circle is _____.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 274<sup>O</sup><span> </span><span> </span>b. 114<sup> O</sup><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">c. 137<sup> O</sup><span> </span>d.72<sup> O</sup><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">______8.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 179px; margin-left: 12px; margin-top: 2px; position: absolute; width: 312px; z-index: -4;"><img height="179" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image042.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1046" width="312" /></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 3in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">In the above figure, ΔABC is circumscribed about circle O. If AD =6cm, CF=8cm, and EB=4cm, what is the perimeter of ΔABC?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">a.18 cm <span> </span><span> </span>b. 36cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">c. 72cm<span> </span>d. 192cm<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="position: relative; z-index: -3;"><span style="height: 191px; left: 72px; position: absolute; top: -12px; width: 216px;"><img height="191" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image044.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1047" width="216" /></span></span><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">______9.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 3in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">Chords AB and CD intersects at E. If AE=10, EB=6, CE=8, and ED=x, what is CD?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">a. 15.5<span> </span>b.8<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="height: 157px; left: 0px; margin-left: 72px; margin-top: 16px; position: absolute; width: 228px; z-index: -2;"><img height="157" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image046.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1048" width="228" /></span><span style="font-family: Calibri, sans-serif;">c. 7. 5<span> </span><span> </span>d. 4<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">______10.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 3in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">In the above figure, B, C, D, and E are points on the circles, what is m</span><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">A?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">a. 10 <span> </span>b. 30<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 159px; margin-left: 72px; margin-top: 14px; position: absolute; width: 204px; z-index: -1;"><img height="159" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image048.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1049" width="204" /></span><span style="font-family: Calibri, sans-serif;">c. 50<span> </span>d. 70<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">______11.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">In the above figure, m</span><span style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">A=____<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">a. m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">B <span> </span><span> </span>b. m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">C<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><span style="font-family: Calibri, sans-serif;">c. m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">D<span> </span>d. m</span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">∠</span><span style="font-family: Calibri, sans-serif;">BEC<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;">B. Proving<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span><span> </span>Write a two-column proof.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><sub><span style="font-family: Calibri, sans-serif;"><span> </span><span> </span><span> </span></span></sub><sub><span lang="FIL-PH" style="font-family: 'Adobe Gothic Std B', sans-serif;">↔</span></sub><sub><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></sub></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Given: AC is tangent to circle O to B.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>__<span> </span>__<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>BE </span><span lang="FIL-PH" style="font-family: 'Adobe Fangsong Std R', serif;">≌</span><span style="font-family: Calibri, sans-serif;">BD<span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span></span><sub><span lang="FIL-PH" style="font-family: 'Adobe Gothic Std B', sans-serif;">↔ </span></sub><span style="font-family: Calibri, sans-serif;"><span> </span>__<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Prove: tangent AC ǁ chord DE<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Construction.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>Draw a scalene triangle. Construct the bisectors of its angles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri, sans-serif;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri, sans-serif;">Answer the problem For Mathitinik on page 509 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;"><b><span style="font-family: Calibri, sans-serif;">Summative test 7<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;"><b><span style="font-family: Calibri, sans-serif;">Please Coordinate Geometry</span></b><span style="font-family: Calibri, sans-serif;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span style="font-family: Calibri, sans-serif;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Target Proficiency<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri, sans-serif;">At least 75% of the class should be able to get at least 75% correct items in the test.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif;"><span> </span>II.<span> </span><b>Procedure<o:p></o:p></b></span></div><ol start="9" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="1"><ol start="1" style="margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Check the assignment<o:p></o:p></span></li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;"><span style="font-family: Calibri, sans-serif;">Administer the test:<o:p></o:p></span></li>
</ol></ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 127.5pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Clarify directions and make the necessary corrections on the questionnaire, if any.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 127.5pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Inculcate the importance of honesty<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 127.5pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Let the students take the test.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in; text-indent: 0in;"><b><span style="font-family: Calibri, sans-serif;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span style="font-family: Calibri, sans-serif;">Questionnaire<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Calibri, sans-serif;"><span> </span></span></b><span style="font-family: Calibri, sans-serif;">Solve the following:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Find the slope, the midpoint, and the length of the segment whose endpoints are (6-4) and (2,2).<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">The slope of a line segment – ¼ and one endpoint is (5,1). If the other endpoint is on the y-axis, what are its coordinates?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Once end of a diameter of a circle is (-2,-7) and its center is (3, 0), find the coordinates of the other end of diameter and the equation of the circle in general form.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Prove: The two medians of any isosceles triangle are equal.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Find an equation of the line through the point (2,3) and parallel to the line x+3y-3=0<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Find an equation of the line through the point (-1, -4) and perpendicular to the line x-2y+2=0.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 32.25pt; text-indent: -0.25in;"><span style="font-family: Calibri, sans-serif;"><span>7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri, sans-serif;">Find the center and the radius of the circle x<sup>2</sup> + y<sup>2</sup> + 14x -4y +52=0. Then sketch the circle.</span></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-71557785316259010522011-03-23T18:43:00.000-07:002011-03-23T18:43:54.121-07:00Chapter 7: Coordinate Geometry<div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">Lesson 7.1</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">Cartesian Coordinate System--Recisited</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">(Textbook pages 514-519, 2 sessions)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">I. Mathematical Concepts and Skills</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. The Cartesian coordinate system is consist of two coplanar perpendicular number lines called axes. The point of intersection of the horizontal line (or the x-axis) or the vertical lines(or the y axis) is called the origin. These axes divide the plane into four regions which are called quadrants.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>B. There is on-to-one correspondence between the points on the Cartesian plane and the ordered pairs of real numbers.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C. An ordered pair is a set of two well-ordered real numbers called coordinates.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>D. The coordinated of a point on the Cartesian plane is determined by projecting the points on both axis.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">II. Objectives</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. Name the parts of a Cartesian coordinate plane</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>B. Describe the distance of a point from two given perpendicular lines</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C. Plot the point corresponding to a given pair of coordinates</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>D. Give the coordinates of a given point on the coordinate plane</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>E. Determine the location of a given point on Cartesian coordinate plane</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">III. Values Integration</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Appreciate the contributions of great men of humanity</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">IV. Materials</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Philippine and world map</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Graphing board and colored chalk</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Grid papers</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Picture of Rene Descartes</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">V. Instructional Strategies</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. Exposition</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>B. Guided Discovery</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C. Consolidation and Practice</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">VI. Procedure</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">Session I</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">A. Preliminary Activities</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>1. Check the assignment</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>2. Provide this motivation:</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. Do you know that elephant can dance?</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>B. Do you know how elephants dance?</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Teach the class the elephant dance. Ask them to move five steps to the left, six steps backward, four steps to the right and seven steps forward. This exercise will enhance their sense of direction. Use music if available.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>What directions connote positive numbers? Negative numbers?</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">B. Lesson Proper</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>1. Draw two perpendicular lines on the boars, one horizontal and the other vertical. Put some points anywhere on the plane. Label the points. Ask the students to describe the location of each point as to whether it is above, below, to the right, or to the left of any of the horizontal line or below?</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>2. Make a thorough exposition of the Cartesian coordinate system. Through guided questions, let the students identify important parts of the Cartesian plane such as the x-and -axes, the origin, and the quadrants.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>3. Briefly recall the concept pf one-to-one correspondence. Let the students realize that every point on the Cartesian plane has a corresponding ordered pair of real numbers.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>4. Discuss how to plot on the Cartesian plane. Use Example 1 on page 515 of the textbook. Give more examples.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>5. Discuss how to name the coordinates of the point on the Cartesian coordinate plane . Use Example 2 on page 516. If necessary, give other examples.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>6. Tell the class that the concept locating points on the Cartesian plane was introduced by Rene Descartes. He used this concept in locating and describing places on the map, which is one of his important contributions to humanity. Show a picture of Descartes and briefly relate important facts about him. Give examples of locating a point on the map using the latitude and longitude, and vise versa.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>7. Inculcate the importance of gratitude to those who made great contributions to humanity like Descartes.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>8. Ask the class to consolidate the discussion. Let them answer Mental Mathematics Exercise 7.1 on page 517 of the textbook.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>9. Tell them to work on Written Mathematics of Exercise 7.1 (numbers 1-10) on page 517 of the textbook.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">C. Assignment</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Work on the Written Mathematics of Exercise 7.1 (numbers 11-20) on page 518 of the textbook.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">Session 2</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">A. Preliminary Activities</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>1. Check the assignment.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>2. Give these reinforcement exercises.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Plot each point on the Cartesian coordinate plane.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. (5 , -8)<span class="Apple-tab-span" style="white-space: pre;"> </span>B. ( -1, 6)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C. (3 , 7)<span class="Apple-tab-span" style="white-space: pre;"> </span>D. (-4 , -2)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>E. (O , -8)<span class="Apple-tab-span" style="white-space: pre;"> </span>F. (9 , 0)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Name the coordinate of each point.<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. A</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>B. B</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C. C</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>D. D<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>E. E</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>F. F</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">B. Follow-up Lesson</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>1. Make a brief recall of the quadrants of the Cartesian coordinate plane. Introduce the terms abscissa and ordinate. Tell the class that the abscissa are the x-coordinate and the ordinates are the y-coordinates.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span"><span class="Apple-tab-span" style="white-space: pre;"> </span>2. Ask them to give the abscissa and ordinates of the following ordered pairs.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>(2 , 7)<span class="Apple-tab-span" style="white-space: pre;"> </span>(-8 , 6)<span class="Apple-tab-span" style="white-space: pre;"> </span>(11 , 0)<span class="Apple-tab-span" style="white-space: pre;"> </span>(4, -10) ( 0, 9)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>3. Divide the class in groups of 5 and let each group perform the activity below. Give each group a grid paper.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. Plot each of the following points:</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A ( 2, 7)<span class="Apple-tab-span" style="white-space: pre;"> </span>B ( 3-, 6)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C (5 , -4)<span class="Apple-tab-span" style="white-space: pre;"> </span>D ( -3, -8)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>E ( 0, 4)<span class="Apple-tab-span" style="white-space: pre;"> </span>F ( -6, -2)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>G ( -10, 0)<span class="Apple-tab-span" style="white-space: pre;"> </span>H ( 9, 1)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>I (-8 , 1)<span class="Apple-tab-span" style="white-space: pre;"> </span>J (1, -5)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>B. Complete the table below.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-tab-span" style="white-space: pre;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">Points<span class="Apple-tab-span" style="white-space: pre;"> </span>Sign of Abscissa<span class="Apple-tab-span" style="white-space: pre;"> </span>Sign of Ordinate<span class="Apple-tab-span" style="white-space: pre;"> </span>Locatio</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">A ( 2, 7)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">B ( -3, 6)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">C (5 , -4)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">D ( -1, -8)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">E ( 0, 4)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">F ( -6, -2)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">G ( -10, 0)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">H ( 9, 1)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">I (-8 , 1)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">J (1, -5)<span class="Apple-tab-span" style="white-space: pre;"> </span></span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>4. Discuss the results of the activity by asking them to observe the table. Ask them to draw conclusions. Focus their attention on the signs of the coordinates and the location of the point.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>5. Let the students answer Written Mathematics of Exercise 7.1 (numbers 11-20) on page 518 of the textbook.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>6. Ask them to work in pairs in solving Written Mathematics of Exercise 7.1 (numbers 21-23) on page 519 of the textbook.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">C. Checking for Understanding</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>1. Plot the following :</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. M ( 6, -2)<span class="Apple-tab-span" style="white-space: pre;"> </span>B. N (-4, -8)<span class="Apple-tab-span" style="white-space: pre;"> </span>C. P (0, -5)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>2. Name the coordinates of the points on the Cartesian coordinate plane.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>3. Determine the location of each point without plotting them.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>A. (-68, 72)<span class="Apple-tab-span" style="white-space: pre;"> </span>B. (-91, -108)</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>C. (168, -76)<span class="Apple-tab-span" style="white-space: pre;"> </span>D. y=0, x > 0</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>E. x <0, y >0<span class="Apple-tab-span" style="white-space: pre;"> </span>F. x > 0, y > 0</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>G. x= 0, y < 0</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>H. positive abscissa, negative ordinate</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>I. Abscissa and ordinate having the same sign</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>J. Abscissa and ordinate are both unsigned</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>For fast learners, ask them to solve the Challenge Problems of Exercise 7.1 on page 519 of the textbook.</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><br />
</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;">D. Assignment</span></span></b></div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><b><span style="font-family: Arial; font-size: 10pt;"><span class="Apple-style-span" style="font-family: 'times new roman', 'new york', times, serif;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Work on Written Mathematics oof Exercise 7.1 (numbers 24-28) on page 519 of the textbook.</span></span></b></div><br />
<b><span style="font-family: Arial; font-size: 10pt;">Lesson 7.2<o:p></o:p></span></b></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Arial; font-size: 10pt;">The Slope of a Line<o:p></o:p></span></b></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><span style="font-family: Arial; font-size: 10pt;">(Textbook pages 520-531, 2 sessions)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">I. Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">A. The slope of a nonvertical line that passes through P</span><span style="font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">(<i>x</i></span><i><span style="font-size: 10pt;">₁</span></i><i><span style="font-family: Arial; font-size: 10pt;">,y</span></i><i><span style="font-size: 10pt;">₁</span></i><span style="font-family: Arial; font-size: 10pt;">) and P</span><span style="font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">(x</span><span style="font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">, y</span><span style="font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">) is m= </span><span style="font-family: Arial; font-size: 10pt;"> or m= </span><span style="font-family: Arial; font-size: 10pt;"> .<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">B. A line with positive slope is pointing upward to the right while a line with negative slope is pointing upward to the left. A horizontal line has zero slope and for vertical lines, the slope is undefined.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">C. The slope <i>m </i>of a nonvertical segment is equal to the slope of the line containing it.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">D. Graphically, the slope of a line is determined by getting the ratio of the change in<i>y</i> to the change in <i>x</i>.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">II. Objectives<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">A. Define the slope of a line<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">B. Find the slope of a line given two of its points<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">C. Find the slope of a segment<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">D. Determine through the graph whether a line has a positive, negative, or zero slope<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">E. Determine graphically the slope of the line<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">F. Graph a line given a point on a line and its slope.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><st1:stockticker><b><span style="font-family: Arial; font-size: 10pt;">III</span></b></st1:stockticker><b><span style="font-family: Arial; font-size: 10pt;">. Values Integration<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Inculcate the value if perseverance<b><o:p></o:p></b></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">IV. Materials<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">graphing board, colored chalk, straight edge<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> grid papers<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> prepared illustrations of lines drawn on Cartesian planes<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> pictures of three boys climbing mountain with different degrees of steepness.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">p. 149<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">V. Instructional Strategies<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">A. Exposition<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">B. Consolidation and Practice<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">VI. Procedure<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">Session I<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">A. Preliminary Activities<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Check the assignment<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Motivation<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. Ask: “Who among you had experienced mountain climbing?”<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Arial; font-size: 10pt;">b. Show the pictures of three boys climbing a mountain. Ask them to observe the position of the three boys.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Arial; font-size: 10pt;">c. Assuming the three boys start climbing at the same time, who do you think could be the first to reach the top, disregarding other factors.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Arial; font-size: 10pt;">d. Students must realize that the pictures shown are mere representations of steepness of lines.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Discuss the importance of perseverance<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">B. Lesson Proper<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">1. Draw three lines on the board similar to those on page 520 of the textbook. Use these illustrations to compare the steepness between lines. Tell the students that the numerical value assigned to the steepness of the line is referred to as slope.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">2. Tell the students that the slope can be computed using the formula is m= </span><span style="font-family: Arial; font-size: 10pt;"> or m= </span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">The formula suggests the need to determine the two points on a line so as to get the slope. Discuss Examples 1 and 2 on pages 522-524 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Ask the class why the slope of a line is represented by <i>m</i>.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">4. Discuss briefly the slope of a segment. Use Examples 3 and 4 on pages 524-525 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">5. Ask the class to consolidate the discussion, then let them answer Written Mathematics of Exercise 7.2 (number 1—6) on pages 530-531 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 150<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">C. Assignment<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Work on Written Mathematics of Exercise 7.2 (numbers 7-16) on page 530 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">Session 2<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">A. Preliminary Activities<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Check the assignment<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Give these reinforcement exercises.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Find the slope of the line that passes through each pair of points.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. (-2, 0). (6)3 b. (3,-10)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> c. (5, -1), (4,5) d. (3.6)(3,10)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">Plot each pair of points in the exercises above them graph the lines that pass through each pair.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">3. Tell the students to observe each graph and their corresponding slope.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> How can you relate the slope of a line to its graph?<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">B. Follow-up Lesson<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">1. Use the exercises above to make a throughout exposition of the graphs of lines with positive, negative, zero, or undefined slopes.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">2. Post on the board the prepared illustration similar to the illustration on page 526 of textbook<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">3. Discuss how to graph a line given a point on a line and its slope. Use example on page 557. Give other examples.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">4. Ask them to stand up and teach them to use their hands and feet to represent lines with positive, negative, zero, and undefined slopes.<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><span style="font-family: Arial; font-size: 10pt;">Page 151<o:p></o:p></span></div><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">C. Checking for Understanding<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Find the slope of the line that passes through each pair of points.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">1. (3,-4),(-2,) 2. (-1, -5), (1, 3)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">3. (1, 3), (7, 12) 4. (4, -2), (7, 3)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">5. (5, -1), (-3, 2) 6. (-3, 6), (9, -18)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">Find the value of the unknown so that the line that passes through the given pair of points will have the given slope.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">7. (2, 1), (4, y); m=1/2 8. (x, 1), (2, -2); m=-3/5<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">9-10. Determine if the points A(-4, -1), B(-2, 1), and C(2, 5) are collinear.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> For the fast learners, ask them to solve the Challenge Problems on page 531.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">D. Assignment<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Work on Written Mathematics of Exercise 7.2 (numbers 17-22) on page 531 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Arial; font-size: 10pt;">Lesson 7.3<o:p></o:p></span></b></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Arial; font-size: 10pt;">Linear Equations<o:p></o:p></span></b></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><span style="font-family: Arial; font-size: 10pt;">(Textbook pages 532-538, 2 sessions)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">I. Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">A. The standard form of the equation of a line is Ax+ By= C, where A,B,C are real numbers.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> B. If the points P</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">(x</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">, y</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">) and P</span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">(x</span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">, y</span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">) are on the line, then its equation may be written in the form<o:p></o:p></span></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><span style="font-family: Arial; font-size: 10pt;">y</span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">-y</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">= y</span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">-y</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">/x </span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">-x</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">(x</span><span style="font-family: 'Cambria Math'; font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">-x</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 152<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> C. If m is the slope of a line and b is its y-intercept, then its equation can be written in the form y = mx+b.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> D. If P</span><span style="font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">(x</span><span style="font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">, y</span><span style="font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">) is a point on a line whose slope is m, then its equation can be written in the form<o:p></o:p></span></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><span style="font-family: Arial; font-size: 10pt;">y</span><span style="font-size: 10pt;">₂</span><span style="font-family: Arial; font-size: 10pt;">-y</span><span style="font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">= m(x-x</span><span style="font-family: 'Adobe Caslon Pro'; font-size: 10pt;">₁</span><span style="font-family: Arial; font-size: 10pt;">)<o:p></o:p></span></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">II. Objectives<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">A. Derive the different forms of the equation of a line<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> B. Rewrite a linear equation of the form Ax + By = C in the form y=mx+b, and vice versa.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> C. Obtain the equation of a line given the following:<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 1. two points<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. slope and one point<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. slope and y-intercept and its graph<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><st1:stockticker><b><span style="font-family: Arial; font-size: 10pt;">III</span></b></st1:stockticker><b><span style="font-family: Arial; font-size: 10pt;">. Values Integration<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Include all the value of obeying laws<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">IV. Materials<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Graphing board, colored chalk<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Grid papers<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Acetate or prepared board work for generalizations and exercises<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">V. Instruction Strategies<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">A. Use of Puzzles (jumbled words)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> B. Discussion<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> C. Consolidation and Practice<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">VI. Procedure<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> Session 1<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> A. Preliminary Activities<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Check the assignment.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Provide these puzzles<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Rearrange the scrambled letters to form a word. A description of the word on the right serves as hint.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. POLES- ratio of the “rise” to the “run.”<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> b. TINTCREPE- the intersection of the graph and an axis.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> c. TIPON- part of a graph<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><span style="font-family: Arial; font-size: 10pt;">Page 153<o:p></o:p></span></div><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Provide a quick review of the different properties of equality.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 4. Inculcate the importance of obeying laws.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">B. Lesson Proper<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Lead the students in recalling the standard form of the linear equation.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Discuss Example 1 on page 532<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Use these additional exercises on transferring equations in standard form. Use flash cards.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. y= -3x +4 b. 7x+ 2y- 3= o<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> c. x= 2y-3 d. 2x-y/ 2= 1<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> e. 4x-2 = 3y f. 1= 3x/2 – y<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> g. ½ x- 1/3= 4/5 y<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Answer Mental Mathematics of Exercise 7.3 (numbers 1-10) on page 537 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 4. Present Examples 2 and 3 on pages 532- 534.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 5. Make use of the standard equation of the line in deriving the equation of a line that passes through the given<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> point with the given slope.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> a. (9, 0), m= 2 b. (2, 4), m= 1<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> c. (2, 4), m= -3 d. (6, 3), m= ½<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> e. (0, 4), m= -3/5 f. (-6, -4), m= 2/3<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">6. Encourage the students to graph the lines above.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">C. Assignment<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Work on Written Mathematics of Exercise 7.3 (numbers 1-10) on page 537 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 154<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">Session 2<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">A. Preliminary Activities<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Check the assignment<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Give these reinforcement exercises.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Find the equation of a line that passes through the given points with the given slope.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. (4, 6), m= 1 b. (-2, 1), m= -2<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> c. (7, -4), m= -1/2 d. (-3, -8), m= -1<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> e. (1, 3), m=3 f. (4, -1/2), m= 4/3<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">B. Follow-up Lesson<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">1. Discuss how to find the equation of a line through two points given points. Present Example 4 on page 535. If<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> necessary, provide additional examples.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">2. Make use of the standard form of the equation of the line in deriving the slope-intercept form of the equation of <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> the line.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">3. Present Example 5 on page 536<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">4. Let the students answer Mental Mathematics of Exercise 7.3 (numbers 11- 20) on page 537 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">5. Let the students work in pairs in solving these seatwork exercises. Obtain the equation of a line given the <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> following:<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> a. m=3, b= -7<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> b, m= -8/7, (4, -7)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> c. (5, 2), (7, 6)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> d. m= -1/2, b= 2<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> e. m= -1, b= 3<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><span style="font-family: Arial; font-size: 10pt;">Page 155<o:p></o:p></span></div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 267px; margin-left: 435px; margin-top: 12px; position: absolute; width: 239px; z-index: -24;"><img height="267" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/06/clip_image006.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="Picture_x0020_2" width="239" /></span><span style="font-family: Arial; font-size: 10pt;">Determine the equation of a line of the following graphs:</span></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="135"></td><td align="left" rowspan="2" valign="top"><br />
</td></tr>
<tr><td height="7"></td></tr>
</tbody></table><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"><o:p></o:p></span></span><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</span><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="8" width="111"></td><td width="11"></td><td width="10"></td><td width="11"></td><td width="440"></td><td width="11"></td></tr>
<tr><td height="6"></td><td colspan="4"></td><td align="left" rowspan="2" valign="top"><br />
</td></tr>
<tr><td height="7"></td><td align="left" rowspan="2" valign="top"><br />
</td></tr>
<tr><td height="2"></td></tr>
<tr><td height="25"></td></tr>
<tr><td height="12"></td><td colspan="2"></td><td align="left" valign="top"><br />
</td></tr>
</tbody></table><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</span><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div><br />
<div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><span style="font-family: Arial; font-size: 10pt;">Page 156<o:p></o:p></span></div><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">C. Checking for Understanding<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 1. Obtain the equation of the line in slope- intercept form given the following slope and y-intercept of the line.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. m= -1, b= -4 b. m=-1/2, b= 4 c. m=2, b=1/2<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Determine the slope and y- intercept of each equation.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="height: 228px; margin-left: 363px; margin-top: 10px; position: absolute; width: 204px; z-index: -22;"><img height="228" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/06/clip_image012.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="Picture_x0020_3" width="204" /></span><span style="font-family: Arial; font-size: 10pt;"> a. -4x + y= 9 b. x= 3+ 2y c. 12= 6x +3y<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Determine the equation of each line in a standard form.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"><br />
</span><span class="Apple-style-span" style="font-family: Arial;">ge 157</span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="19" width="103"></td><td width="127"></td><td width="287"></td><td width="63"></td></tr>
<tr><td height="130"></td><td colspan="2"><br />
</td><td align="left" rowspan="3" valign="top"><br />
</td></tr>
</tbody></table><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</span><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 4. Obtain the equation of a line in standard form given the following:<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. y- intercept: 7, slope: -2<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> b. x- intercept: -6, slope: 3<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> c. slope: -7/2, (3, -1)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> d. (4, 0), (7, 2)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> For fast learners, ask them to solve the Challenge Problems on page 538 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">D. Assignment<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Work on Written Mathematics of Exercise 7.3 (numbers 11-24) on page 538 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 159<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Arial; font-size: 10pt;">Lesson 7.4<o:p></o:p></span></b></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span style="font-family: Arial; font-size: 10pt;">Parallel and Perpendicular Lines<o:p></o:p></span></b></div><div align="center" class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><span style="font-family: Arial; font-size: 10pt;">(Textbook pages 539-547, 3 sessions)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">I. Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">A. If two nonvertical lines intersect, then their slopes are not equal.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> B. If two nonvertical lines have different slopes, then the lines are intersecting.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> C. If two nonvertical lines are parallel, then the slopes are equal.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> D. If two lines which do not coincide have the same slope, then the lines are parallel,<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> E. If two nonvertical lines are perpendicular, then their slopes are negative reciprocals.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">II. Objectives<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> A. Determine algebraically the point of intersection of two lines.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> B. State and apply theorems on the slopes of intersecting, parallel and perpendicular lines.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><st1:stockticker><b><span style="font-family: Arial; font-size: 10pt;">III</span></b></st1:stockticker><b><span style="font-family: Arial; font-size: 10pt;">. Values Integration<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Think logically<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">IV. Materials<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Graphing board, colored chalk, straightedge<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Grid papers<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Visual aids on the theorems and corresponding proofs.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">V. Instructional Strategies<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">A. Review<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> B. Exposition<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> C. Discussion<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> D. Consolidation and Practice<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">VI. Procedure<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> Session 1<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> A. Preliminary Activities<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1, Check the assignment<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 160<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Motivation<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. To enhance the students’ logical thinking skills, let them try this activity:<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> “How can two identical squares be cut so the pieces can be rearranged to form bigger square?”<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="8" width="207"></td><td width="98"></td><td width="29"></td><td width="98"></td></tr>
<tr><td height="98"></td><td align="left" valign="top"><br />
</td><td></td><td align="left" valign="top"><br />
</td></tr>
</tbody></table><div class="NoSpacing"><span class="Apple-style-span" style="color: #222222; font-family: Arial; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> <b>B. Lesson Proper<o:p></o:p></b></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Recall how to determine the intersection of two lines algebraically. Use Examples 1-3 on pages 539- 541 of the <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 46.5pt;"><span style="font-family: Arial; font-size: 10pt;">textbook. Ask the students to get the slopes and graph each example on the board. Guide the students to realize that the slopes can be used to determine whether the two lines are intersecting or parallel.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">2. State and prove Theorem 7-1 and Theorem 7-3 with proper illustrations. State also the converse of the two<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> Theorems.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Working in pairs, ask the students to graph the following on their grid paper: y= 2x+1 and y= 1/2x +3.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Ask them to graph the two lines on one Cartesian plane. Discuss the graphs and lead them to the idea that the<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> slope of perpendicular lines are negative reciprocals of each other. State Theorem 7-5.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">4. Discuss Examples 4 and 5 on pages 543-545.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">5. Ask the students to consolidate the discussion. Then let them answer Mental Mathematics of Exercise 7.4 on <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Arial; font-size: 10pt;"> page 546.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">C. Assignment<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Prove Theorem 7-4 and Theorem 7-5<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">Session 2<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">A. Preliminary Activity<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Ask somebody to explain the proofs of Theorem 7-4 and 7-5. Give the incentives to those who could prove <o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> each theorem.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 161<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt;">2. Give the following reinforcement exercises.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Determine if the pair of lines are parallel, perpendicular or neither.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> a. y= 6x+3 b. y= 3/4x- 5<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> y= 6x-1 3x-y = 6<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> c. 4x-y = 7 d. 2x+ y = 6<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> x+4y= 7 3x-y= 6<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> e. 2x+ 5y = 8 f. x-4y = 8<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 5x-2y= 7 2x- 4y = 8<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> Plot the following points and connect them from A to D.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> A(1, 3) B (5, 1) C(7, 5) D(3, 7)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">B. Follow-up Lessons<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. By using a protractor and a ruler, help the students see that the figure is actually square.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Ask them to get the slopes of pairs of opposite sides and also the slopes of pairs of consecutive sides. Let<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> them realize that the slopes can be used to determine whether a polygon is a square, rectangle, parallelogram,<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> or a right triangle.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 3. Discuss the exercises in Written Mathematics of Exercise 7.4 on pages 546- 547 (numbers 1 and 2, 5 and 6)<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">C. Assignment<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">Work on Written Mathematics of Exercise 7. 4 (numbers 3,4 and 7) on pages 546- 547 of the textbook.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">Session 3<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;">A. Preliminary Activities<o:p></o:p></span></b></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Arial; font-size: 10pt;"> </span></b><span style="font-family: Arial; font-size: 10pt;">1. Check the assignment<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;"> 2. Make a brief recall of the point- slope form and standard form of a line.<o:p></o:p></span></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Arial; font-size: 10pt;">Page 162<o:p></o:p></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="NoSpacing" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><br />
</div></div><div class="NoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="NoSpacing" style="color: #222222;"><br />
<div class="Section1" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><div class="MsoNormal">3. Give the following reinforcement exercises:</div><div class="MsoNormal">Determine if the quadrilateral with the following vertices is a parallelogram:</div><div class="MsoNormal">P (-4, 5) , Q (4, 6) , R (8,-1) , S (-2,-4)</div><div class="MsoNormal">Determine if the triangle with the given vertices is a right triangle.</div><div class="MsoNormal">R (-4,-5) , V (1, 0) , Q (-6,-3)</div><div class="MsoNormal"><b>B. Follow up Lesson<o:p></o:p></b></div><div class="MsoNormal">1. Through the experience, present the solutions to written Mathematics of Exercise 7.4 (numbers 8-14) on page 547 of the textbook.</div><div class="MsoNormal">2. Ask the class to work in pairs in solving Written Mathematics of Exercise 7.4 (numbers 15-17) on page 547 of the textbook.</div><div class="MsoNormal"><b>C. Checking for Understanding<o:p></o:p></b></div><div class="MsoNormal">1. Determine if the pair of lines are parallel, perpendicular, or neither.</div><div class="MsoNormal" style="text-indent: 0.5in;">a. y = -5x + 7 b. 2 x + 6y – 8 = 0</div><div class="MsoNormal"> y = x – 3 3 x + 9 y + 3 = 0<o:p></o:p></div><div class="MsoNormal"> c. 3 x + 5 y = 10 d. 4 x – 7 y = 8<o:p></o:p></div><div class="MsoNormal"> 3 x – 5 y = 2 7 x + 4 y = 14<o:p></o:p></div><div class="MsoNormal"><br />
</div><div class="MsoNormal">2. (2, 7), (- 2, - 1), (6, 5) are vertices of a right triangle. Is this a right triangle?</div><div class="MsoNormal">3. (-2, 1), (3, 3), (5, 0), (-1, -2) are vertices of a quadrilateral. Is this a parallelogram?</div><div class="MsoNormal">4. Write an equation in standard form of the line passing through the given point and parallel to the given line.</div><div class="MsoNormal"> (4, 5); 5 x – 3 y = - 15</div><div class="MsoNormal"> 5. Write an equation in standard form of the line passing through the given point and parallel to the given line.</div><div class="MsoNormal"> (- 1, - 2); 3 x – 2 y = 6</div><div class="MsoNormal">6. The line containing points (- 6, k) ang (4, 3) is perpendicular to the line containing points (13, 1) and (9, k + 1). Find K.</div><div class="MsoNormal">D. Assignment</div><div class="MsoNormal"> Work on Written Mathematics of Exercise 7.4(numbers 18-21) on page 547 of the texbook.</div><div class="MsoNormal"><br />
</div><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-size: 12pt; line-height: 18px;">Lesson 7.5<o:p></o:p></span></b></div><div align="center" class="MsoNoSpacing" style="text-align: center;"><b><span style="font-size: 12pt;">The Distance Formula<o:p></o:p></span></b></div><div align="center" class="MsoNoSpacing" style="text-align: center;"><i><span style="font-size: 8pt;">(Textbook pages 548-555, 1 session)<o:p></o:p></span></i></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.5in;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical Concept and Skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.75in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If x₁ and x₂ are the coordinates of <i>A</i> and <i>B</i>, respectively, on a horizontal number line, then the distance between A and B is AB = lx₁ - x₂l.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If y₁ and y₂ are the coordinates of <i>C</i> and <i>D</i>, respectively, on a vertical number line, then the distance between <i>C</i> and <i>D </i> is CD = ly₂ - y₁l.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The distance between two points P₁(x₁, y₁) and P₂(x₂, y₂) is </div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.5in;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Find the distance between two points on the same horizontal or vertical line.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Derive the distance formula using the Pythagorean Theorem</div><div class="MsoNoSpacing" style="margin-left: 1.5in;">Use the distance formula to determine the distance between any two points on the Cartesian Plane.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.5in;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice self-assessment or introspection</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.5in;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1in;">Graphing board, colored chalk</div><div class="MsoNoSpacing" style="margin-left: 1in;">Meter stick, ruler</div><div class="MsoNoSpacing" style="margin-left: 1in;">Acetate or prepared board work for generalizations and exercise</div><div class="MsoNoSpacing" style="margin-left: 1in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.5in;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Expositions</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guided Discovery</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Consolidation</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.5in;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.75in;"><b>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the permission from the immediate superior in conducting the activity in a basketball court, field or open space near the classroom.</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Construct an arrow diagram or a number line on the floor.</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Divide the class equally into two groups. Decide who will be the first one to play and the one to ask questions.</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>During the game, the first group to play must assign members on each coordinate. Representative from the opponent will ask question. The answer will be determined by the player assigned to the coordinate being asked. Coaching from the members will not be allowed. At the count of 10 after the question was asked, he answer must be given by the player assigned on the coordinate. The player must sit down. Otherwise the score will be given to the other group and it will be their turn.</div><div class="MsoNoSpacing" style="margin-left: 1.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Provide a quick review on integers and absolute value.</div><div class="MsoNoSpacing" style="margin-left: 1in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><b>Lesson Proper</b></div><div class="MsoNoSpacing" style="margin-left: 1in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discuss how to find the distance between 2 points on a number line through inductive approach. Provide as many examples as you can until the student can generalize how to find the distance between two points on a number line.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Present examples 1 in pages 549-550. If necessary give 3 pairs of coordinates, say (1, - 5) and (-1, -6) and allow a student to graph it and another student to compute the distance.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Let them answer Mental Mathematics of Exercise 7.5 on page 553 of the textbook.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guide them to derive a formula for finding the distance between two points using the Pythagorean Theorem.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Give an Example where two points are not on horizontal line or vertical line such as the following pairs of two points found in Example 2 on pages 551-552. Draw it in a graphing board for emphasis.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Make use of the distance formula to explain the solutions made for Example 1.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Let them work in pairs in Answering Written Mathematics of Exerices 7.5(numbers 1-10 on page 554 of the textbook.</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1.5in;">Work on Written Mathematics of Exercise 7.5 (numbers 11 – 20) on page 554 of the textbook.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.5in;"><b>Session 2<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activitires<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Relate a brief account of Pythagoreas?</div><div class="MsoNoSpacing"><br />
</div><div align="center" class="MsoNoSpacing" style="margin-left: 1.25in; text-align: center;">Pythagoras (ca.</div><div align="center" class="MsoNoSpacing" style="margin-left: 1.25in; text-align: center;">540 B.C.)</div><div class="MsoNoSpacing" style="margin-left: 1.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in;">Very little is known about Pythagoras. He was a leader of a secret society or school founded in the 6<sup>th</sup> century B.C. This group, known as Pythagoreans, considered it impious for a member to claim any discovery for himself. Instead, each new idea was attributed to their founder, Pythagoras. This was more than school ; it was a philosophy and a way of life . Every evening , each member of the Pythagorean society had to reflect on three questions:</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>What good have I done?</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Where have I failed?</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>What have I not done that should have done?</div><div class="MsoNoSpacing" style="margin-left: 1.5in;">Ask your students to reflect on the same questions. Every student can share his answer to a partner.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Give these reinforcement exercises.</div><div class="MsoNoSpacing" style="margin-left: 1.25in;">Find the distance between the following points.</div><div class="MsoNoSpacing" style="margin-left: 1.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(-2, 1), (-8, 1) c. (3, 7), (-11, 7)</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(-2, 5), (0, 5) d. (14, 2), (14, -5)</div><div class="MsoNoSpacing" style="margin-left: 1.5in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><b>Follow –up Lesson.</b></div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Present Example 3 on pages 552-553. Guide the students in analyzing and giving conclusions. Emphasize that a graph helps facilitate solving a problem.</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Use exposition in solving this problem:</div><div class="MsoNoSpacing" style="margin-left: 1.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in;">Show that triangle with the vertices <i>A (3, -6), B (8, -2), and C (-1, 1)</i>is a right triangle. Find the perimeter of ∆<i><span style="font-size: 10pt;">ABC.<o:p></o:p></span></i></div><div class="MsoNoSpacing" style="margin-left: 1.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in;">The students should be able to prove that ∆<i><span style="font-size: 10pt;">ABC </span></i>is a right triangle by showing that the square of the longest side is equal to the sum of the squares of the other sides. To determine the perimeter, let them add the lengths of the 3 sides.</div><div class="MsoNoSpacing" style="margin-left: 1.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1.25in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Form groups of 4. Assign these exercises to each group</div><div class="MsoNoSpacing" style="margin-left: 1.5in;">Group number Written Mathematics D, page 555</div><div class="MsoNoSpacing" style="margin-left: 1.5in; text-indent: 0.5in;">1&6 number 31</div><div class="MsoNoSpacing" style="margin-left: 1.5in;"> 2&7 number 32</div><div class="MsoNoSpacing"><b> </b>3&8 number 33</div><div class="MsoNoSpacing"> 4&9 number 34</div><div class="MsoNoSpacing"> 5&10 number 35</div><div class="MsoNoSpacing"> Let them write the solution on a manila paper and be ready to discuss its solutions.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.75in; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for understanding<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.75in;">Find the distance between each pair of points.</div></div><i style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri, sans-serif; font-size: 11pt;"><br clear="all" style="page-break-before: auto;" /></span></i><br />
<div class="Section2" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><i>A(-4, 2), B (5, 4)</i></div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><i>B(1, 2),C(4, -2)</i></div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>C(4, 2), D(-2, 10)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>D(-6, -2), E(-5, 4)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>E(-5, 0), F(-9, 6)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>F(-2, 4), G(7, -8)</div><div class="MsoNoSpacing"><br />
</div></div><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 18px;"><br clear="all" style="page-break-before: auto;" /></span><br />
<div class="Section3"><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;">7-8. The distance between points (1, 1) and (4, y) is 5. Find all possible values for y.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;">9-10. Find the perimeter of the triangle whose vertices are G (-7, 5), C (-7, -7), and F (2, -7)</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> For fast learners, ask them to solve the Challenge Problems on page 555 of the textbook.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Work in Written mathematics of Exercise 7.5(numbers 21-50) on pages 554-555 of the textbook.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div align="center" class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center;"><b>Lesson 7.6<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center;"><b>The Midpoint Formula<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center;">(<i><span style="font-size: 10pt;">textbook pages 556-563, 2 sessions</span>)<o:p></o:p></i></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Mathematical Concepts and Skills</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The midpoint of a horizontal segment lies between the endpoints. Its ordinate is the ordinate of the endpoints and its abscissa is the average of the abscissas of the endpoints.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The midpoint of a vertical segment lies between the endpoints. Its abscissa is the abscissa of the endpoints and its ordinate is the average of the ordinate s of the endpoints.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If P₁ (x₁, y₁) and P₂ (x₂, y₂) are any two points in a coordinate plane, then the midpoint of P₁ P₂ has coordinates</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1in;"><span class="Apple-style-span" style="font-family: Calibri, sans-serif;"><span class="Apple-style-span" style="font-size: 15px; line-height: 17px;"><br />
</span></span></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Device, state, and apply the midpoint formula</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Determine the midpoint of the segment joining 2 given points</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Strengthen faith in God</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Graphing board, colored chalk, and straight edge</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Visual aids in different illustration</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"> That will help device the midpoint formula</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Visual aids on different examples</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Manila paper and crayons or pens</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guided Discovery</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Deductive Approach</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Exposition</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discussion</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Consolidation and Practice</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Start with a prayer. After praying, ask what can be obtained from praying. Ask the class to relate stories related to the power of prayers.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignments</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Motivation</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Present the following situation</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in;">A Painter plans to create an abstract piece of art. He wants to stars at the center of his rectangle canvas. He plots a scale drawing on the coordinate axes and he assigns the vertices of the rectangles as follows: A (0, 0), B (12, 0), C (12, 8), and D (0, 8). How can he locate the center of this rectangular canvass?</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Use paper folding in illustrating midpoint of diagonals and sides of quadrilateral, and the center of a circle.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Proper<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Show illustrations of horizontal and vertical segments drawer on Cartesian plane. For each segment, guide them how to determine the abscissa and the ordinate of the midpoint. Use the examples given in the textbook on pages 556-557.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Emphasize the following about midpoint of a segment</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Midpoint M of segment AB lies on AB and AM = MB</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The midpoint divides a segment into two segment s of equal lengths.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>With proper illustration, guide the students in the deprivation of the Midpoint formula. You may use the presentation in the textbook on pages 557-558.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discuss Example 1 on page 559. Ask them to go back to the problem posed at the star t of the discussion. Let them find out if their given answers are correct.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the class to consolidate the discussion, then let them answer Mental Mathematics of Exercise 7.6 on page 561 of the textbook.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Let them work in pairs solving Written Mathematics of Exercise 7.6(A, numbers 1-5,and B,1-5) on pages 562 of the textbook.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><b> Assignment</b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Work on Written Mathematics of Exercise 7.6 (A, numbers 6-10 and B, 6-10) on page 562 of the textbook.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b>Session 2<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.<b><o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Give those reinforcement exercises.<b><o:p></o:p></b></div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Find the midpt. Of the segment joining the given pairs of points.</div><div class="MsoNoSpacing" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><br />
</div></div><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 18px;"><br clear="all" style="page-break-before: auto;" /></span><br />
<div class="Section4" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(3, -6), (3, 8)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(-4, -6), (-2, -9)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(4, 8), (2, -8)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(7, -9),(4, 8)</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">e.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(-5, -4), (-11, -22)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">f.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(2 ½ , 3) (4 ½ , 2 ½ ) </div><div class="MsoNoSpacing"><br />
</div></div><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 18px;"><br clear="all" style="page-break-before: auto;" /></span><br />
<div class="Section5" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><div class="MsoNoSpacing">If M is the midpt of PQ, determine the coordinates of Q.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">a. M (1,-2), P (3, -6) B. M (-1, 5), P (3, 8)</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>B. Follow up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">1. Briefly recall the following:</div><div class="MsoNoSpacing"> A. medians of triangle</div><div class="MsoNoSpacing"> B. Kinds of parallelograms</div><div class="MsoNoSpacing"> C. Distance formula</div><div class="MsoNoSpacing"> D. Perimeter</div><div class="MsoNoSpacing">2. Discuss Example 2 on pages 560-561.</div><div class="MsoNoSpacing">3. Form eight groups of students. Let each group solve one of the problems of Written Mathematics of Exercises 7.6 (C, numbers 1-4)</div><div class="MsoNoSpacing">On page 562. Then let them discuss the solutions to the class.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>C. Checking for Understanding<o:p></o:p></b></div><div class="MsoNoSpacing" style="text-indent: 0.25in;">1. Find the midpoint of the segment with the given endpoints.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> (27, -36), (77, -102)</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(-4.72, 1.04), (-5.20, -5.36)</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(-1 ⅓, -2), (⅓, 2)</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>(2x + y, -x +3y), (3y, -x +y)</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.25in;">2. If M is the midpoint of PQ, determine the coordinates of Q.</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.25in;">a. M (0, 0), P (-3, -1)</div><div class="MsoNoSpacing" style="margin-left: 0.25in;">b. M (3 1/2 , -7) P (3, -8)</div><div class="MsoNoSpacing" style="margin-left: 0.25in;">c. M (1 ½, ½ ), P (5, -5)</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.25in;">3. Solve the following.</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"> The vertices of a quadrilateral are (2, -10), (-4, -2), (8, -5) and (2, 3). Show that the diagonals of a quadrilateral bisect each other.</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"> For fast learners, let them solve the Challenge Problems on page 263.</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><b>D. Assignments<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><b> </b>Work in Written Mathematics of Exercise 7.6 (C, numbers 5 and 6) on page 563 of the textbook.</div><div class="MsoNoSpacing" style="margin-left: 0.25in;"><br />
</div><div align="center" class="MsoNoSpacing" style="margin-left: 0.25in; text-align: center;"><b>Lesson 7.7<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="margin-left: 0.25in; text-align: center;"><b>Coordinate Proofs of Geometric Theorems.</b></div><div align="center" class="MsoNoSpacing" style="margin-left: 0.25in; text-align: center;">(<i>Textbook pages 564-569, 3 sessions</i>)</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b> I. Mathematical Concepts and Skills<o:p></o:p></b></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b> </b>A. “Coordinate Geometry” is about proving theorems by means of placing a given figure in a proper position on the coordinate axes and using algebraic principles and procedures in the process.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"> B. The following are suggested to appropriately place a geometric figure in a coordinate plane:</div><div class="MsoNoSpacing"> 1. Place one of the vertices of the geometric figure at the origin</div><div class="MsoNoSpacing"> 2. Place the sides of the geometric figure along the coordinate axis.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>II. Objectives<o:p></o:p></b></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b> </b>A. Place triangles and quadrilaterals on the Cartesian plane and find the missing coordinates.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"> B. Use coordinates proofs in verifying properties of triangles and quadrilaterals</div><div class="MsoNoSpacing"><b>III. Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing"><b> </b>Show skills in finding ways and means in doing things</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>IV. Materials<o:p></o:p></b></div><div class="MsoNoSpacing"><b> </b>Graphing paper, colored chalk, straightedge</div><div class="MsoNoSpacing"> Grid papers</div><div class="MsoNoSpacing"> Visual aids on most common ways of placing geometric figures on the coordinate axes</div><div class="MsoNoSpacing"> Some properties of triangles and quadrilaterals</div><div class="MsoNoSpacing"> Manila paper and crayons or pentel pens</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>V. Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing"> a. Expositions</div><div class="MsoNoSpacing"> b. Discussions</div><div class="MsoNoSpacing"> c. Guided Proving</div><div class="MsoNoSpacing"> d. Consolidation and Practice</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>VI. Procedure<o:p></o:p></b></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing"><b>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">1. Administer a game on identifying the kinds of quadrilaterals and identifying its properties by plotting points,</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> Ask the students to form five groups. Give different sets of coordinates forming geometric figures, tell the students to plot on the Cartesian plane and identify the figure formed. The first group to identify the figure should state a property of the figure to earn a point. The group that can earn more points will be given incentives.</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> Tell them that the above activity is what we called the Coordinate Geometry. What do you mean by Coordinate Geometry? Entertain the student’s responses.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>B. Lesson Proper<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>State that “Coordinate Geometry refers to the association of real numbers with points and this association makes it possible to prove theorems concerning plane figures by algebraic means. State the steps in proving geometric Theorems using coordinates.<b><o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrate the most common way of placing geometric figures on the coordinate axes as show<b><o:p></o:p></b></div><div class="MsoNoSpacing">a. For Isosceles triangle</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><br />
</div><div align="center" class="MsoNoSpacing" style="text-align: center;"><br />
</div><div class="MsoNoSpacing">b. For Quadrilaterals</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">3. Illustrate examples on finding the missing of figures without using new variables.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">4. Ask the class to consolidate the discussion, then let them answer the mental Mathematics of Exercises 7.7 on page 567 of the textbook.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing"> Work on Written Mathematics of Exercise 7.7 (A, numbers 3 and 4) on page 568 of the textbook.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>Session 2<o:p></o:p></b></div><div class="MsoNoSpacing"><b>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing"><b> </b>1. Check the assignment.</div><div class="MsoNoSpacing"> 2. As a review, give the following exercises.</div><div class="MsoNoSpacing"> Solve for the distance between the following pairs of points.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="text-indent: 0.5in;">a. (-2, -3), (6, 1) b. (3, 4), (-2, 1)</div><div class="MsoNoSpacing" style="text-indent: 0.5in;">Find the midpoint of the segment with the given endpoints.</div><div class="MsoNoSpacing" style="text-indent: 0.5in;">a. (4, 8) b. (-4, -7), (-9, 8)</div><div class="MsoNoSpacing" style="text-indent: 0.5in;"><br />
</div><div class="MsoNoSpacing" style="text-indent: 0.5in;">3. Recall basic concepts related to quadrilateral and triangles, the slopes of paralle; and perpendicular lines.</div><div class="MsoNoSpacing" style="text-indent: 0.5in;"><br />
</div><div class="MsoNoSpacing"><b>B. Follow-up lesson<o:p></o:p></b></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">1. Illustrate the use of coordinate geometry in proving some properties of triangles. Use example 1 on pages 564 -566. Present other examples.</div><div class="MsoNoSpacing" style="margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNoSpacing">2. Give example of proving some properties of quadrilaterals using coordinate Geometry. Use Example 2 on pages 566- 567.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">3. Let the class work in pairs in working on written Mathematics of Exercise 7.7 (b, #568-569) of the textbook</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>C. Checking for Understanding<o:p></o:p></b></div><div class="MsoNoSpacing">Show a coordinate proof for the statement:</div><div class="MsoNoSpacing"> “The midpoint of the hypotenuse of any right triangle is equidistant from each of the 3 vertices</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>D. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing"><b> </b>Work in Written Mathematics of Exercises 7.7(B, #6-10) on page 569 of the textbook.</div><div align="center" class="MsoNoSpacing" style="text-align: center;"><b>Lesson 7.8<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="text-align: center;"><b>Circles in the Coordinate Plane<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="text-align: center;"><i><span style="font-size: 9pt;">(textbook pages 570-580, 3 sessions)<o:p></o:p></span></i></div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing" style="text-indent: 0.5in;"><b>I. Mathematical Concepts and Skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A circle is a set of coplanar points all of which are equidistant from a fixed point called center.</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The standard equation of the circle with radius(r) and center at (0, 0) is</div><div class="MsoNoSpacing" style="margin-left: 1in;">r³ = x² + y².</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The standard equation of a circle with radius (r) and center at my point (h, k) is</div><div class="MsoNoSpacing" style="margin-left: 1in;">r² = (x – h) + (y – k)</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The general form of the equation of a circle is x² + y² + Dx + Ey = 0</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>III. Objectives<o:p></o:p></b></div><div class="MsoNoSpacing"><b> </b>A. Recall the definition of a circle</div><div class="MsoNoSpacing"> B. State and derive the standard form of the equation of a circle with radius (r) and center (h, k)</div><div class="MsoNoSpacing"> C. Find the equation of a circle, given its center and radius and vice versa</div><div class="MsoNoSpacing"> D. Transform the equation of a circle in standard form to an equation in general form and vice versa</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>III. Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing"> Discuss how to be flexible in life</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>IV. Materials<o:p></o:p></b></div><div class="MsoNoSpacing"> Compass</div><div class="MsoNoSpacing"> Meter stick</div><div class="MsoNoSpacing"> Acetate or prepared board work and illustration for generalizations and exercises</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>V. Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Exposition</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guided Discovery</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Consolidation and Practice</div><div class="MsoNoSpacing" style="margin-left: 1in; text-indent: -0.25in;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Cooperative work</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing"><b>VI. Procedure<o:p></o:p></b></div><div class="MsoNoSpacing"><b>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing"><b> A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing"><b> </b>1. Check the assignment.</div><div class="MsoNoSpacing"> 2. Motivation</div><div class="MsoNoSpacing"> Ask the students if they know the rhyme: “Small Circle, Big Circle!”</div><div class="MsoNoSpacing"> Draw on the board while reciting to let them see the figure. Then Together, let the students draw on scratch paper.</div><div class="MsoNoSpacing"><br />
</div><div class="MsoNoSpacing">“Small circle, Big circle!”</div><div class="MsoNoSpacing">Small circle, small circle, Big circle</div><div class="MsoNoSpacing">Small circle, small circle, Big circle</div><div class="MsoNoSpacing">This is papa, this is Mama</div><div class="MsoNoSpacing">Say Goodbye,</div><div class="MsoNoSpacing">Six times Six, Six times Six, equals thirty six</div><div class="MsoNoSpacing">Six times Six, Six times Six, equals say good bye</div></div></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-18779822287861002132011-03-23T18:40:00.000-07:002011-03-23T18:40:06.302-07:00Chapter 6: Circles<div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Calibri;">Lesson 6.1</span></b><span style="font-family: Calibri;"> The Circle (Textbook pages 414-421, 3 sessions)<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">I. <span> </span>Mathematical Concepts and Skills<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">A. <span> </span>A secant is a line that intersects the circle in two points.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">B. <span> </span>A tangent is a line that is coplanar with the circle and intersects the circle in exactly one point.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">C. <span> </span>If a radius is perpendicular to a chord, then it bisects the chord.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">D. <span> </span>If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to the chord.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">E. <span> </span>The perpendicular bisector of a chord passes through the center of the circle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">F. <span> </span>Congruent circles are circles that have congruent radii.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">G. <span> </span>Concentric circles are coplanar circles with the same center.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">H. <span> </span>If chords of a circle or of congruent circles are equidistant from the center(s), then the chords are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">I. <span> </span>If chords of a circle or of congruent circles are congruent, then they are equidistant from the center of the circle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">II.<span> </span>Objectives<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>A. <span> </span>Apply the definitions and concepts related to circles<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">B. <span> </span>Prove and apply the theorems that show the relationship between radius and chord.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">C. <span> </span>Prove and apply the theorem about the perpendicular bisector of a chord.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">D. <span> </span>Identify congruent and concentric circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Calibri;">E. Prove and apply the theorems about chords that are equidistant from the center of the circle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">III. <span> </span>Values Integration<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Love and concern for the other people<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">IV. <span> </span>Materials<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Compact disc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Manila paper<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Markers<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">V. <span> </span>Instructional Strategy<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Discussion<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">VI. <span> </span>Procedure<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">Session 1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">A. <span> </span>Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>1. Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-family: Calibri;">2. Recall the definitions of circles, radius, chord and diameter.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;">B. <span> </span>Lesson Proper<span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">1. <span> </span>Bring a compact disc. Use it as a springboard to the lesson. Tell the students that a CD is 12.5 cm in diameter but the track where the information is coded is thinner than hair that it rotates at a speed of 200 rpm.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">2. <span> </span>Ask the students to give some more examples of objects that suggest circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">3. <span> </span>Ask the students why a ring is used to represent love.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">4. <span> </span>Draw the figure and ask the students to identify the radius, chord, and diameter. Then introduce the terms secant and tangent. Ask the students to compare line EF and line GH. Introduce also the terms interior and exterior of a circle. Ask the students to compare the distance of point I as well as the distance of point J from O with the length of the radius.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 1in;"><span style="font-family: Calibri;">5. <span> </span>Guide the students in proving Theorems 6-1 and 6-3.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>6. <span> </span>Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>a. Prove Theorem 6-2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>b. Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: 0.5in;"><span style="font-family: Calibri;">Solve Written Mathematics of Exercise 6.1 (numbers 1 and 2) on page 423 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>C. <span> </span>Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;"><span style="font-family: Calibri;">Solve Written Mathematics of Exercise 6.1 (numbers 3 and 4) on page 423 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">Session 2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">A. <span> </span>Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;"><span> </span>1. Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;"><span> </span>2. Recall the Hypotenuse-Leg Theorem<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">B. Follow-up Lesson<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;">1. Introduce the concept of congruent circles by considering the following figures<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;"><span> </span>Ask the students which of the above circles are congruent. Ask them to define congruent circles in their own words.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;">2. Introduce to the class concentric circles by drawing on the board a figure similar to the one below.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;">3. Activity<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;"><span style="font-family: Calibri;">a. Draw a circle<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;"><span style="font-family: Calibri;">b. Draw two chords equidistant from the center.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;"><span style="font-family: Calibri;">c. Carefully measure the lengths of two chords.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;"><span style="font-family: Calibri;">d. What do you notice?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>4.<span> </span>Guide the students in proving Theorem 6-4 deductively.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">5.<span> </span>Ask the students to state the converse of Theorem 6-4. Then ask them to prove Theorem 6-5<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">6.<span> </span>Practice exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span style="font-family: Calibri;">a. <span> </span>Answer Mental Mathematics of Exercise 6.1 (numbers 1-10) on page 422 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span style="font-family: Calibri;">b. <span> </span>Solve Written Mathematics of Exercise 6.1 (numbers 5 and 6) on page 423 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">C. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-family: Calibri;">Solve the Written Mathematics of Exercise 6.1 numbers (7 and 8) on page 424 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">Session 3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">A. Preliminary Activity<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Check up the assignment.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">B. Follow-up Lesson<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>1. Illustrative Example<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Explain the proof of this problem on the board.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Given: Radius OA and DC<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>D is the midpoint of chord AC<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Prove: </span><st1:place><span style="font-family: Calibri;">OB</span></st1:place><span style="font-family: Calibri;"> is perpendicular bisector of AC<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-family: Calibri;">2. Practice Exercise<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;"><span style="font-family: Calibri;">Solve Written Mathematics of Exercise 6.1 (numbers 9 and 10) on page 424 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">C. Checking the Understanding.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.1 (numbers 11-15) on pages 424-425 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">D. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><span style="font-family: Calibri;">Solve Written Mathematics of Exercise 6.1 (numbers 16-20) on pages 424-425 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><span style="font-family: Calibri;">If there is enough time, solve Challenge problems of Exercise 6.1 on page 426 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span style="font-family: Calibri;">Lesson 6.2</span></b><span style="font-family: Calibri;"> - Arcs and Angles (Textbook pages 427-446, 3 sessions)<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">I. <span> </span>Mathematical Concepts and Skills<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">A. A central angle is an angle whose vertex is the center of the circle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">B. Minor arc AB is the union of two points A and B and all the points of the circle<span> </span>in the interior <AOB<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">C. Major arc ACB is the union of points Q and B and all points of the circle in the Exterior of Central angle <AOB.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">D. A semicircle is the union of the endpoints of a diameter and all points of the circle that lie on one side of the diameter.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">E. The degree measure of a minor arc is equal to the degree measure of the central angle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">F. The degree measure of a major arc is equal to 360 degrees minus the degree measure of its related minor arc.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">G. The degree measure of a semicircle is 180 degree.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">H. The measure of an arc formed by two adjacent, nonoverlapping arcs is the sum of the measures of the measures of the two arcs.<span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">I. In the same circle of in congruent circles, arcs which have the same measures are congruent arcs.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">J. If two minor arcs of a circle or of congruent circles are congruent, then the corresponding chords are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">K. If two of a circle or congruent circles are congruent, then their corresponding minor arcs are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">L. If two central angles of a circle or of congruent circles are congruent, then the corresponding minor arcs are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">M. If two minor arcs of a circle or of congruent circles are congruent, then the corresponding central angles are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">N. If two central angles of a circle or of congruent circles are congruent, then their chords are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">O. If two chords of a circle or of congruent circles are congruent, then the central angles are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">II. <span> </span>Objectives<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>A. To illustrate and define the following:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>1. central angle<span> </span>2. Minor arc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Calibri;">3. Major arc<span> </span>4. Semicircle<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Calibri;">5. Degree measure of minor arc<span> </span>6. Degree measure of major arc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span style="font-family: Calibri;">7. Degree measure of semicircle<span> </span>8. Congruent arc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">B. To illustrate and apply the Arc addiction postulate.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;">C. To prove and apply the theorems about arcs and central angles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">III. <span> </span>Values Integration<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Friendship<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">IV. <span> </span>Materials<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Manila paper<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Marker<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">V. <span> </span>Instructional Strategy<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Whole Class Discussion<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">VI. <span> </span>Procedure<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Session 1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">A. Preliminary Activity<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;">Check the assignment.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;">B. Lesson Proper<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;"><span> </span>1. Introduce the following terms. Use the figure on page 427 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -9pt;"><span style="font-family: Calibri;"><span> </span>a. Central Angle<span> </span>b. Minor Arc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;">c. Major Arc<span> </span>d. Semicircle<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;">e. Degree measure of minor arc<span> </span>f. Degree measure of major arc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;"><span style="font-family: Calibri;">g. Degree measure of semicircle<span> </span>h. congruent arc<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;">2. Illustrate how to use the Arc Addition Postulate<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;">3. Associate Arc Addition Postulate with making friends with other students.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;">4. Guide the students in proving Theorem 6-6<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;">5. Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;"><span> </span>a. Prove Theorem 6-7<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><span style="font-family: Calibri;">b. Prove Theorem 6-8<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><span style="font-family: Calibri;">c. Prove Theorem 6-9<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">C. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Prove Theorems 6-10 and 6-11. Refer to pages 431-432 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">Session 2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">A.<span> </span>Preliminary Activity<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">B. <span> </span>Follow-up Lesson<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;"><span> </span>1. Draw the following figures on the board.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; text-align: center;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.25in;"><span style="font-family: Calibri;">Ask the students to compare <AOB of Circle O and <ABC of circle O. After making it clear with the students that <ABC is an inscribed angle, ask the students to define an inscribed angle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;">2. Copy the figure on the board:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.25in;"><span style="font-family: Calibri;">Ask the students to measure <ABC and <APC. Ask the students to write a formula for m<ABC in terms of <APC. Then ask them to write a formula for m<ABC in terms of arc AC.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;">3. Guide the students in proving Theorem 6-12.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;">4. Illustrative Example<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.25in;"><span style="font-family: Calibri;">Use the example on page 442 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;">5. Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: 9pt;"><span style="font-family: Calibri;"><span> </span>a. <span></span>Answer Mental Mathematics of Exercise 6.2 (numbers 1-10) on page 442 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: 9pt;"><span style="font-family: Calibri;">b. <span> </span>Solve Written Mathematics of Exercise 6.2 (numbers 1-4) on page 443 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">C. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.25in;"><span style="font-family: Calibri;">Solve Written Mathematics of Exercise 6.2 (numbers 5-10) on page 443 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">Session 3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">A. <span> </span>Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">1. Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">2. Recall Theorem 6-12 and the definition of a right angle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">B. <span> </span>Follow-up Lesson<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;">1.<span> </span>a.<span> </span>Guide the students in proving Corollary 6-12.1.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;"><span> </span>An angle inscribed in a semicircle is a right angle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;"><span style="font-family: Calibri;"><span> </span>b. Explain the proof of Corollary 6-12.4.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;"><span> </span>If two arcs of a circle are inscribed between parallel secants, then the arcs are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">2. <span> </span>Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>a. Prove the following:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Corollary 6-12.2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>If two inscribed angles intercept the same arc or congruent arcs, then the angles are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Corollary 6-12.3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Opposite angles of an inscribed quadrilateral are supplementary.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span style="font-family: Calibri;">b. Solve Written Mathematics of Exercise 6.2 (numbers 11-14) on pages 443-444 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">C.<span> </span>Checking for understanding<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.2 (numbers 15-20) on pages 443-444 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">D. <span> </span>Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.2 (numbers 21-28) on pages 443-445 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>If there is enough time, solve for the challenge problem of Exercise 6.2 on page 446 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><b><span style="font-family: Calibri;">Lesson 6.3 </span></b><span style="font-family: Calibri;">- Tangent lines and Tangent Circles (Textbook pages 447-459, 4 sessions)<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;">I. Mathematical Concepts and Skills<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">A. <span></span>If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">B. <span></span>If a line is perpendicular to a radius at its outer endpoint, then it is tangent to the circle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">C. <span></span>If two segments from the same external point are tangent to a circle then the two segments are congruent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">D. <span></span>Two circles are tangent to each other, if and only if they are coplanar and are tangent to the same line at the same point.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">E. <span></span>Two circles are externally tangent, if and only if each lies in the exterior of the other except for the point of tangency.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">F. <span> </span>Two circles are internally tangent, if and only if one of them lies in the interior of the other except for the point of tangency.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">G. <span></span>If two circles are tangent, then their centers and their point of tangency are collinear.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">H.<span> </span>A common tangent is a line that is a tangent to each of two coplanar circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">I. <span> </span>A common internal tangent is a common tangent that intersects the segment joining the centers of two circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">J. <span> </span>A common external tangent is a common tangent that does not intersect the segment joining the centers of two circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="font-family: Calibri;">II. <span> </span>Objectives<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">A. <span></span>To prove and apply the theorems about tangent lines to circle<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">B.<span> </span>To define the following terms:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>a.<span> </span>tangent circles<span> </span>b. <span> </span>externally tangent circles<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>c. <span> </span>internally tangent circles<span> </span>d. <span> </span>common tangent<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>e. <span> </span>common internal tangent<span> </span>f. <span> </span>common external tangent<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-family: Calibri;">C. <span></span>To prove if two circles are tangent, then their centers and the point of tangency are collinear.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">III. <span> </span>Values Integration<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Concern for others<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">IV.<span> </span>Materials<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Activity sheets<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">V. <span></span>Instructional Strategies<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>A.<span> </span>Whole class discussion<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>B. <span></span>Small group discussion<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">VI. <span></span>Procedure<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Session 1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>A.<span> </span>Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>1. Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>2. Recall indirect proof.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>B. <span></span>Lesson Proper<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>1.<span> </span>Activity<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>a. <span> </span>Draw a circle. Name its center O.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>b. <span> </span>Draw a line tangent to the circle at point A.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>c.<span> </span>Draw OA. What part of circle is OA?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>d.<span> </span>Using your protractor, determine whether the tangent is perpendicular to<span> </span>OA. What can you conclude?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>2. <span> </span>Guide the students in proving Theorem 6-13 and using indirect proof.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>3.<span> </span>Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -1in;"><span style="font-family: Calibri;"><span> </span>a.<span> </span>Divide the class into smaller groups. Assign the best in the class to be the leaders in each group. Tell them to help those who find proving geometric statements difficult. Tell them also that showing concern for other people is a virtue that they should possess as future leaders. Ask the class to prove Theorem 6-14.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -1in;"><span style="font-family: Calibri;"><span> </span>b. <span> </span>Answer Mental Mathematics of Exercise 6.3 (numbers 1-10) on pages 454-455 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -1in;"><span style="font-family: Calibri;"><span> </span>c. <span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 1-4) on page 455 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -1in;"><span style="font-family: Calibri;"><span> </span>C. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -45pt;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 5 and 6) on page 456 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -45pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;">Session 2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;">A. <span></span>Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;"><span> </span>1.<span> </span>Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;"><span> </span>2.<span> </span>Recall the Hypotenuse-Leg Theorem.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;">B.<span> </span>Follow-up Lesson<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;"><span> </span>1. <span> </span>Guide the students in proving Theorem 6-15<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><span style="font-family: Calibri;"><span> </span>2. <span> </span>Illustrative Example<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;"><span> </span>AB and BC are tangent to circle O at A and C, respectively. If BA=12 and OA=9, find BC, and </span><st1:place><span style="font-family: Calibri;">OB.</span></st1:place><span style="font-family: Calibri;"><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-align: center;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><span style="font-family: Calibri;">3. <span> </span>Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 7 and 8) on page 456 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>C. <span></span>Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><span style="font-family: Calibri;">Solve Written Mathematics of Exercise 6.3 (numbers 7 and 8) on page 456 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;">Session 3<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;">A. Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>1. <span> </span>Check the assignment.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>2. <span> </span>Recall the definition of collinear points.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;">B.<span> </span>Lesson Proper<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>1. <span> </span>Arrange the students in pairs. Then ask them to do the following activities:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>Activity 1<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>a. <span> </span>Draw a circle. Name the center P.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.25in;"><span style="font-family: Calibri;"><span> </span>b. <span> </span>Draw a line tangent to circle P at any point R on the circle.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>c. <span> </span>Draw another circle tangent to the same line at same point of tangency. In how many ways can this be done?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>d. <span> </span>Draw a line through the center of the circles and the common point of tangency. What do you observe?<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>2. <span> </span>After doing Activity 1, ask the students to define tangent circles, externally tangent circles and internally tangent circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>3. <span> </span>Discuss the proof of Theorem 6-16.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Activity 2<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>a.<span> </span>Draw a circle. Name the center of your circle O.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>b. <span> </span>Draw another circle that does not intersect the first one. Name the center P.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>c. <span> </span>Join the centers of the two circles by a segment.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>d.<span> </span>Draw a line tangent to both circles that:<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri;">Intersect the segment joining the centers of the two circles<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span style="font-family: Calibri;">Does not intersect the segment joining the centers of the two circles.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>4. <span> </span>After doing Activity 2, ask the students to define common tangent, common internal tangent, and common external tangent.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>5.<span> </span>Illustrative Example<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>Use the example on page 453 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>6.<span> </span>Practice Exercise<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.75in;"><span style="font-family: Calibri;"><span> </span>Solve Written mathematics of Exercise 6.3 (numbers 11 and 12) on page 457 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">C. Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 13 and 14) on page 457 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">Session 4<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">A.<span> </span>Preliminary Activities<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Check the assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">B. <span></span>Follow-up Lesson<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>1.<span> </span>Illustrative Example<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Explain the proof of this problem.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Given: Secant AE and DE intersecting at B and C.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Prove: Triangle ACE is similar to Triangle DBE<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span><o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span class="Apple-style-span" style="font-family: Calibri;"><br />
</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">2. <span> </span>Practice Exercises<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 15 and 16) on page 458 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">C. <span></span>Checking for Understanding<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 17 and 18) on page 458 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;">D. <span></span>Assignment<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>Solve Written Mathematics of Exercise 6.3 (numbers 19 and 20) on page 458-459 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: 0.25in;"><span style="font-family: Calibri;">If there is enough time, solve Challenge problems of exercise 6.3 on page 459 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><b><span style="font-family: Calibri;">Lesson 6.4 </span></b><span style="font-family: Calibri;">Angles formed by Tangents and Secants<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family: Calibri;">I. <span> </span>Mathematical Concepts and Skills<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>A. <span></span>If two secants intersect in the interior of a circle, then the measure of the angle formed is equal to one-half of the sum of the measures of the intercepted arcs.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>B. <span></span>If two secants intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>C. <span></span>The measure of an angle formed by a secant and a tangent intersecting in the exterior of a circle is one-half the positive difference of the measures of the intercepted arcs.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>D. <span></span>The measure of an angle formed by a secant and a tangent intersecting in the exterior of a circle is one-half the positive difference of the measures of the intercepted arcs.<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: -0.5in;"><span style="font-family: Calibri;"><span> </span>E.<span> </span>The measure of an angle formed by two tangents to the same circle is one-half the positive difference of the measures of the intercepted arcs. </span></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-88036262344125993122011-03-23T18:38:00.000-07:002011-03-23T18:38:07.385-07:00Chapter 5<div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">c. Construct two nonoverlapping triangles with different bases between the two parallel lines.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">d. Represent the altitude of each triangle by <i>h </i>and their respective bases by <i>b<sub>1</sub></i> and<i>b<sub>2.</sub></i></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">e. Find the ratio of the areas of the two triangles.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">f. What can you conclude?</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span>Tell the students that in doing the given activities, they should rely on their own abilitiesand judgment.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">2. Guide the students in proving Theorem 5-1 and 5-2 and in completing the proof of Basic Proportionality Theorem.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">3. Illustrative Examples</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span>Use the examples on page 366 of the textbook.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">4. Practtice Exercises</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span>a. Answer Mental Mathematics of Exercise 5.2 (numbers 1-10) on page 368 of the textbook.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span>b. Solve Written Mathematics of Exercise 5.2 (numbers 1-7) on page 368 of the textbook.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span lang="FIL-PH">C. Assignment<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span>Solve Written Mathematics of Exercise 5.2 (numbers 8-10) on page 369 of the textbook.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span lang="FIL-PH">Session 2<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check the assignment.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the Law of Proportion</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 71.25pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Guide the students in proving the Converse of the Basic Proportionality Theorem.</span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 71.25pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.2 (numbers 11 and 12) on page 369 of the textbook.</span></div><div class="MsoListParagraph" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Checking for Understanding<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.2 (numbers 13-16) on page 369 of the textbook.</span></div><div class="MsoListParagraph" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.2 (numbers 17-20) on page 370 of the textbook.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span lang="FIL-PH">Lesson 5.3<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span lang="FIL-PH">Similarity Between Triangles<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span lang="FIL-PH"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Similar polygons are polygons in which the corresponding<span> </span>angles are congruent and the ratios of the lenghts of the corresponding sides are equal.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Two triangles are similar, if and only if the corresponding angles are congruent and the lenghts of the corresponding sides are proportional.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If there exists a correspondence between the vertices of two triangles such that three angles of one triangle are congruent to the corresponding angles of the second triangle, respectively, then the two triangles are similar.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If two angles of a triangle are congruent to two angles of the second triangle, respectively, then the two triangles are similar.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Similarity between triangles is an equivalence relation.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If a triangle is similar to a second triangle and a second triangle is congruent to a third triangle, then the first triangle is similar to the third triangle.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If two pairs of corresponding sides of two triangles are propotional and the included angles are congruent , then the two triangles are similar.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If all three pairs of corresponding<span> </span>sides of two triangles are proportional, then the two triangles are similar.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span lang="FIL-PH"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrate and define similar polygons and similar triangles</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Prove and use the AAA similarity and AA Similarity Theorems to draw conclusions about triangles</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Show that similarity between triangles is an equivalence relation</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Prove that if a triangle is similar to to a second triangle and a second triangle is congruent to a third triangle, then the first triangle is similar to the third triangle</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Prove and use the SAS Similarity and SSS Similarity Theorems to draw conclusions about triangles</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span lang="FIL-PH"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Values Integration<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">Self-confidence is necessary to accomplish desired result</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span lang="FIL-PH"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Materials<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">Picture of similar figures</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">Manila paper</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">Marker</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span lang="FIL-PH"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Instructional Strategies<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Whole Class Discussion</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.5in;"><b><span lang="FIL-PH"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Procedure<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH">Session 1<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check the Assignment.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the congruence Postulate for Trianlges</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Lesson Proper<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Show the class pictures having the same shape but differnt sizes, Ask the students afterward to describe the pictures.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Then present the following geometric figures:</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 3in;"><br />
</div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH"><span> </span><span> </span>C.<span> </span></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="12" width="409"></td></tr>
<tr><td></td><td><br />
</td></tr>
</tbody></table><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 6.5in;"><span style="height: 22px; left: 0px; margin-left: 415px; margin-top: 68px; position: absolute; width: 21px; z-index: 251667968;"><br />
</span><span style="height: 15px; left: 0px; margin-left: 360px; margin-top: 45px; position: absolute; width: 16px; z-index: 251664896;"><br />
</span><span style="height: 2px; left: 0px; margin-left: 36px; margin-top: 82px; position: absolute; width: 17px; z-index: 251653632;"><br />
</span><span style="height: 50px; left: 0px; margin-left: 353px; margin-top: 40px; position: absolute; width: 84px; z-index: 251646464;"><br />
<br />
</span><span style="height: 32px; left: 0px; margin-left: 46px; margin-top: 68px; position: absolute; width: 30px; z-index: 251644416;"><span> </span><span> </span><span> </span></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 6.5in;"><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><tbody>
<tr><td height="13" width="60"></td><td width="2"></td><td width="99"></td><td width="2"></td></tr>
<tr><td height="21"></td><td align="left" valign="top"><br />
</td><td></td><td align="left" valign="top"><br />
</td></tr>
</tbody></table><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><o:p> </o:p></span></span><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</span><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br clear="ALL" /></span><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">Ask the students to describe the geometric figures.</span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in; text-indent: 0in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Tell the students that the last pairs of geometric figures are examples of similar polygons. Ask them to define similar polygons.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in; text-indent: 0in;"><span lang="FIL-PH"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Consider the two triangles below .</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><span lang="FIL-PH"><span> </span></span><span> </span><span> </span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in; text-indent: 4.5pt;"><span lang="FIL-PH">Ask the students to describe the triangles.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in; text-indent: 0in;"><span lang="FIL-PH"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Ask the students to complete the proofs of AAA Similarity and AA Similarity Theorems. Tell the students that they should have self-confidence in accomplishing the task given to them.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in; text-indent: 0in;"><span lang="FIL-PH"><span>6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrative Examples</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">Use the examples on page 372 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Practice Exercises</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><span lang="FIL-PH">Answer Mental Mathematics of Exercises 5.3 (numbers 1-10)<span> </span>on pages 380-382 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><span lang="FIL-PH">Solve Written Mathematics of Exercises 5.3 (numbers 1-6) <span> </span>on pages 382 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Solve Written<span> </span>Mathematics of Exercise 5.3 (numbers 7 and 8) on pages 383 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in;"><b><span lang="FIL-PH">Session 2<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check the assignment.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the Poin Plotting Theorem and the Line Postulate .</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Questions</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Ask the students to complete the proof of the SAS Similarity Theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Guide the students in proving the SSS Similarity Theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH"><span> </span>Solve Written Mathematics of Exercise 5.3 (number 11) on page 383 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Solve the Written Mathematics of Exercise 5.3 (number 11) on page 383 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in;"><b><span lang="FIL-PH">Session 3<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check the assignments</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the following:</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">AA Similarity</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">SAS<span> </span>Similarity Theorem</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">SSS Similarity<span> </span>Theorem</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Questions</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrative Example</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Show how to prove this problem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Given : <i>AB is perpendicular to BD<o:p></o:p></i></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><i><span lang="FIL-PH"><span> </span>EC is perpendicular to CD<o:p></o:p></span></i></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Prove : triaangle ABD is congruent to triangle ECD</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><span lang="FIL-PH">Solve written mathematics of exercise 5.3 (numbers 12 and 13) on page 384 of the text book.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Checking for Understanding</span></b><span lang="FIL-PH"></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span>Solve written mathematics of exercise 5.3 (numbers 14-20) on page 384 of the text book.<span> </span></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignments</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH">Study the Proof of the right Triangle Similarity Theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span lang="FIL-PH">Lesson 5.4<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><b><span lang="FIL-PH">Similarities in Right Triangle<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">In any right triangle, the altitude to the hypotenuse divides the triangle into two right triangles which are similar to each other and to the given right triangle.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">In a right triangle, the altitude to the hypotenuse is the geometric mean of the segments into which it divides the hypotenuse and each of the leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">In an isoceles right triangle, the lenght of the hypotenuse is equal to the lenght of the leg times square root of 2.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">In a 30-60-90 triangle, the length of the hypotenuse is twice the lenght of the shorter leg and the lenght of the longer leg is square root of 3 times the length of the shorter leg.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><b><span lang="FIL-PH">II.<span> </span>Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 76.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Find the lengths of sides and altitudes of rifgt triangles</span></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 76.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Apply relationships in Isoceles Right Triangle Theorem and right 30-60-90 degrees triangles.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><b><span lang="FIL-PH">III. Values Integration<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><span lang="FIL-PH"><span> </span>Impotance of cooperation</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><b><span lang="FIL-PH">IV. Materials<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><span lang="FIL-PH">marker</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><span lang="FIL-PH">Manila paper</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><b><span lang="FIL-PH">V.<span> </span>Instructional Strategies<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><span lang="FIL-PH"><span> </span>A. Whole Class Discussion</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><span lang="FIL-PH"><span> </span>B. Small Essay <span> </span>Discussion</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><b><span lang="FIL-PH">VI.<span> </span>Procedure<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 58.5pt;"><b><span lang="FIL-PH">Session 1<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 76.5pt; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 112.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check assignments.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 112.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the Pythagorean Theorem</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 76.5pt; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Lesson Proper<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Ask the students to solve the following problems.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt;"><span lang="FIL-PH">If in triangle ABC, angle ACB is a right angle , line<span> </span>CD is the hypotenuse to line AB, A is a 60 degrees angle and angle ACD is 30 degrees, find angle DCB and angle B.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Ask the following questions:</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 112.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Into how many triangles is the given triangle divided by its hypotenuse?</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 112.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Are the two triangles congruent? Similar? Why?</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 112.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Are the two triangles similar to the original triangle? Why?</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Divide the class into small groups.Remind them about<span> </span>the importance of cooperation in doing a task. Then tell them to prove the Right Triangle Similarity theorem and the Geometric Mean Theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrative Examples.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt;"><span lang="FIL-PH">Use the examples on page 388 of the book</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 94.5pt; text-indent: -0.25in;"><span lang="FIL-PH"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Answer<span> </span>Mental Mathematics of Exersice 5.4 (numbers 1-10) on page 390 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.4 ( numbers 1-9) on page 390 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 76.5pt; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 76.5pt;"><span lang="FIL-PH"><span> </span>Solve Written Mathematics of Exercise 5.4 (numbers 10-19) on page 391 0f the textbook.</span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span lang="FIL-PH"><span> </span><span> </span><b>Session 2<o:p></o:p></b></span></div><div class="MsoListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary<span> </span>Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check the assignment.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the Pythagorean Theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Prove the Isoceles Rigth Triangle Theorem and the 30 dergee, -60 degree, -90 degree Triangle Theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Illustrative Example<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><span lang="FIL-PH">Find the perimeter of triangle ABC.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.4 (number 20) on page 319 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Checking Understanding<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.4 <span> </span>(number 21) on page 391 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 4.5pt; text-indent: 85.5pt;"><span lang="FIL-PH">Solve Written mathematics o f Exercises 5.4 (number 22) on page 391 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 4.5pt; text-indent: 85.5pt;"><br />
</div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 4.5pt; text-align: center;"><b><span lang="FIL-PH">Lesson 5.5<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 4.5pt; text-align: center;"><b><span lang="FIL-PH">Consequences of the Basic Proportionality Theorems; Areas and Perimeters of Similar Figures<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 4.5pt; text-align: center;"><br />
</div><div align="center" class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 4.5pt; text-align: center;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If each of the three or more coplanar parallel lines are each cut by two transversals, the intercepted segments on the two trnsversals are proportional.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">The bisector of an angleof a triangle separates the opposite sides into segments whose lengths are proportional to the lengths of the other two sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Two corresponding altitudes of similar triangles are proportionalto the corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Any two corresponding angle bisectors of similar triangles are proportional to the corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Any twocorresponding medians of similar triangles are proportional to the corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">The ratio of the perimeters of two similar triangles is equal to the ratio of any pair of corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">If two triangles are similar, then the ratio of their areas equals the square of the ratio of the lrngths of any corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">The ratio of the areas of two similar triangles is equal to the square of the ratio of the two corresponding<span> </span>perimeters.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH">II.<span> </span>Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">To prove and apply the theorems about three or more parallel lines cut by a transversal</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">To prove and apply the Theorem about the bisector of an angle of a triangle</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">To prove and apply the theaorems about proportional segments in triangles</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">To prove and apply the theorems about perimeters and areas of similar triangles</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH">III. Values Integration<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH"><span> </span></span></b><span lang="FIL-PH">The need for self-confidence in performing a task</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH">IV. Materials<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH"><span> </span></span></b><span lang="FIL-PH">Manila paper</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH"><span> </span>Marker</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH">V. Instructional Strategies<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH"><span> </span></span></b><span lang="FIL-PH">A. Whole class discussion</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH"><span> </span>B. Practice</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH">VI.<span> </span>Procedure<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b><span lang="FIL-PH"><span> </span>Session 1<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check assignments</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the basic Proportionality Theorem</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Lesson Proper</span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Ask the students to solve the following problems</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Suppose in the above figur, the transversal <i>t<sub>1</sub></i> is moved the right, will the value of QRr change as well as a result of the movement?</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Guide the students in proving that if each three or more coplanar parallel lines are cut by two transversals, the intercepted segments of the two transversals are proportional.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrative Example</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH"><span> </span>Answer Written <span> </span>Mathematics of Exercises 5.5 (numbers 1-10)<span> </span>on page 406 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Answer Written Mathematics of Exercises 5.5 (numbers 1-2)<span> </span>on page 406 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><span lang="FIL-PH">Solve written Mathematics of Exercise 5.5 (number 3) on page 406 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in;"><b><span lang="FIL-PH">Session 2<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check the assignment.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the definition of an angle bisector.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Questions<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Guide the students in proving the following theorem:</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">The bisector of an angle of a triangle separates the opposite sides into segments whose lengths are proportional to the lengths of the two other sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrative Example</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">In triangle ABC, ray AD bisects angle BAC.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">If AB is 8,AC is 10, and BC is 6 find BD and DC</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice Exercises</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Solve written mathematics of exercises 5.5 (number 4)on page 406 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.5 (number 5) on page 406 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in;"><b><span lang="FIL-PH">Session 3<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary<span> </span>Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Check assignments</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Recall the AA Similarity Theorem</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Questions<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Guide the students in proving the following theorems:</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Any two corresponding<span> </span>altitudes of similar triangles are proportional to the corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Any two corresponding angle bisectors of similar triangles are proportional to the corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Tell the students that they should have sel-confidence whenever they are asked to prove any geometric statement</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">Prove the following:</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Any two corresponding medians of similar triangles are proportional to the corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span lang="FIL-PH"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">The ratio of the perimeters of two similar triangles is equal to the ratio of any pair of corresponding sides.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Complete the proof of Theorem 5-20.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0in;"><b><span lang="FIL-PH">Session 4<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><span lang="FIL-PH">Check assignment.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><span lang="FIL-PH">Recall the Geometric mean Theorem.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Prove th pythagorean Theorem using the geometric Mean theorem.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Introduce the Pythagorean Triples.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Illustrative Example</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span lang="FIL-PH">Find the perimeter and area of triangle ABC.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="FIL-PH"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="FIL-PH">Practice exercise</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.5 (number 7) on page 407 of the text book.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Checking for Understanding<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b><span lang="FIL-PH"><span> </span><span> </span></span></b><span lang="FIL-PH">Solve Written Mathematics of Exercise 5.5 (number 8) on page 407 of the textbook.</span></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: -0.25in;"><b><span lang="FIL-PH"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="FIL-PH">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><span lang="FIL-PH">Solve Written Mathematics Exercise 5.5 (numbers 9 and 10) on page 407 of the textbook.</span></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-83420322657708096472011-03-23T18:35:00.001-07:002011-03-23T18:35:54.656-07:00Chapter 4:<div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">IV. Materials</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>Manila paper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>Marker]</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">V. Instructional Strategy</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;">Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">VI. Procedure</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Session 1</div><ol start="1" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Introduce the three special kinds of parallelograms.</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Direct the students on explore on page 308 of the textbook.</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Prove Theorem 4-6: The diagonals of a rectangle are congruent</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Practice Exercises</li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: 0.25in;">Prove:</div><ol start="4" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="1"><ol start="1" style="margin-top: 0in;" type="a"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Theorem 4-7: Each diagonal of a square bisects a pair of opposite angles</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Theorenm 4-8: The diagonals of a rhombus are perpendicular</li>
</ol></ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">VII. Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>Prove Theorems 4-9 and 4-10</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Sessions 2</div><ol start="1" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Preliminary activities</li>
<ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Check the assignment</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Recall the SAS Postulate and theorem 2-8</li>
</ol><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Follow-up Lessons</li>
<ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Guide the students in proving Theorem 4-11: If the diagonals of a parallelogram is a rhombus.</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Illustrative Examples</li>
</ol></ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>ABCD is a parallelogram</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">AE =2x + 10 and CE= 6x-30</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Find AC</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;"><img height="81" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1025" width="228" /></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-align: center;">93</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Given: JGNS is a rectangle</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt;">E is the midpoint JS</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt;">Prove: GEN is isosceles</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt;"><img height="124" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1026" width="222" /></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt;"><br />
</div><ol start="2" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><ol start="3" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Practice Excercises</li>
</ol></ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Answer Mental Mathematics of excercises 4.2 (numbers 1-6 ) on page 311 of the textbook</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Solve Written Mathematics of Exercise 4.2 (numbers 1-8) of the textbook on page 312 of the textbook.</div><ol start="3" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Checking for Understanding</li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;">Solve Written Mathematics of Exercise 4.2 (numbers 9-14) on pages 312-313 of the textbook.</div><ol start="4" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Assignment</li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;">Solve Written Mathematics of Exercise 4.2 (numbers 15-20) on pages 312-313 of the textbook</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center;">If There is enough time, Solve Challenge Problems of Exercise 4.2 on page 314 o the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center;">Lesson 4.3</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center;">Conditions<span> </span>Guaranteeing that a Quadrlateral is a parallelogram</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center;">(Textbook pages 315-327)</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Mathematical Concepts and Skills</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If bith pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center;">94</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If the diagonals of a quadrilaterals bisect each other , then the quadrilateral is a parallelogram.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The segment that joins the midpoints of two sides of a triangle is parallel to the third side and is one half of its measure.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Objectives</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">A, Prove that a quadrilateral is a parallelogram</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">B. Apply the mid-segment Theorem in problem solving.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.5in;">III. . Values Integration</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>Determination in attaining a goal</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Materials</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Rulers</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Protractors</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Graphing paper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Instrutional Strategies</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practical work</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Procedure</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Session 1</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">!. Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">2. Recall the definitions of parallelogram, Postulate 15, and the congruence postulates for trangles</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">B. Lesson proper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">!. Tell the students to state the converse of corollary 4-1.2 and Theorems 4-3 and 4-4</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">2. Ask the students to investigate the converses using rulers, protractors, and graphing paper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">3. Prove the converses of corollary 4-1.1, Theorems 4-3, and 4-4.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">4. Illustrate how to use these converses to prove that a quadrilateral is a parallelogram.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center;">95</div><ol start="5" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Discuss the proof of theorem 4-12.</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Practice excercises</li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;">Prove Theorems 4-13, 4-14, and 4-15.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt;">Solve Written Mathematics of Excercises 4.3 (numbers 1-6) on page 321 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Session 2</div><ol start="1" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Preliminary Activities</li>
<ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Check the assignments</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Recall Theorems 2-1. the definitions of between and the definition of midpoint.</li>
</ol><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Follow-up Lesson</li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;">!. Arange the students in pairs, then ask them to do the following activities.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Draw any triangle and name it ABC</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Find the midpoint of side AB and label it G</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Find the midpoint of <st1:place w:st="on"><st1:city w:st="on">Side</st1:city> <st1:state w:st="on">BC</st1:state></st1:place> and label it E</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Draw segment GE</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>e.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Find the length of GE and the length of AC</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>f.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Compare their lengths</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>g.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Is segment GE parallel to side AC? WHY?</div><ol start="2" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><ol start="2" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Guide the students in proving the mid-segment Theorem.</li>
<li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">illustrative Example</li>
</ol></ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Use the example on page 321 of the textbook.</div><ol start="2" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><ol start="4" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Practice Excercises</li>
</ol></ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Answer mentalMathematics of Exercise 4.3 (numbers 1-14) on pages 322 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Solve Written Mathematicn he Exercise 4.3 (numbers 7-8) on pages 324-3125 of the textbook.</div><ol start="3" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-top: 0in;" type="A"><li class="MsoNormal" style="margin-bottom: 0.25em; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-indent: 0px;">Assignment</li>
</ol><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;">Solve Written Mathenatics of Excercises 4.3 (numbers 9-13) on the pages 324-325 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center;">96</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in;">/session 3</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the ssignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall the definitions of parallelogram and Theorems 4-12, and 4-13, 4-14, 4-15.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Follow-up Lesson</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Illustrative Examples</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">Write and Explain the proof of this problem on the board.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">Given: DE <span style="font-family: Symbol;"><span>@</span></span> AF</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span> </span><span> </span>DE <span style="font-family: Symbol;"><span>½<span>½</span></span></span> AF</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span> </span><span> </span>EC <span style="font-family: Symbol;"><span>@</span></span> FB</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span> </span><span> </span>EC<span style="font-family: Symbol;"><span>½<span>½</span></span></span> FB</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><img height="97" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image005.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_i1027" width="313" /></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practice Excercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Solve Written<span> </span>Mathematics of Excercises 4.3 (numbers 14 and 15) on page 325 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Checking for understanding</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Solve Written Mathematics of exercise 4.3 (numbers16 and 17) of page 325 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Solve Written Mathematics of Excrcise 4.3 (numbers 18=24) on page 326-327 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;">If there is enough time, Challenge Problems of exercise 4.3 on page 327 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;">97</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;">Lesson 4.4</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;">The trapezoid and its properties</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-align: center;">(textbook pages 324 337, 2 sessions)</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Mahematical Concepts an d skills</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A trrapexoid is a quadrilateral with exactly one pair of parallel sides</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>An isoscleles trapezoid is a trapezoid are congruent</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The base abgles of an isosceleles trapezoid are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The diagonals of an isosceles trapezoid are congruent</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If the base angles of trapezoid are congruent, then the trapezoid id isosceles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If the diagonals o a trapezoid are congruent, the trapezoid is isosceles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The median of a trapezoid is the segment joining the midpoints of the legs.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The median of a trapezoid is parallel to its bases</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The median of a trapezoid is half the sum of the lengths of the bases</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>ii.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Objectives</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Identify and define a isosceles trapezoid</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Apply inductive and deductive skills to derive a certain properties of the trapezoid</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Apply the Theorem about trapezoid</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Values Integration</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">The importance of cooperation in performing a task</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Materials</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Rulers</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Sticks</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Instructional Strategies</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practical Work</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.5in;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Procedure</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">Session 1</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 135pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 135pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall the definition opf a trapezoid and Theorem 4-5.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-align: center;">98</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Lsson Proper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">!. Ask the students to from<span> </span>pairs, distribute four sticks to each pair two cks should have congruent lengths.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">2. Have each pair construct a trapezoid</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">3. Tell them to do the following</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span> </span>a. Find the lengths of the legs in centimeters</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span> </span>b. lengths of the diagonbals in centimeters</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><span> </span>b. lengths of the measures of the base angles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.5in;">4. When the strudents are finished doing the activity, ask each pair to tell the class about their trapezoid (It is expected that some of them will be able to construct an isosceles trapezoid)</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.5in;">5. Ask the students to define an isosceles trapezoid and to enumerate some of its properties.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.5in;">6. Guide the students I n proving theorem 4-17.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.5in;">7. Illustrative Examples</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.5in;"><span> </span>a. Prove Theorem 4-20</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: 0.5in;"><span> </span>b. Complete the proof of theorem 4-19.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>C. Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>Prove Theorem 4-20</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Session 2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">A, Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>1. Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>2. Recall the Mid-degment Theorem</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">B. Follow-up Lesson</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>1. Guide the students in proving Theorem 4-21</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>2. Ask the students to work on Expllore on page 332 of the t3extbook</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>3. Illustrative Example</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>Use the example on page 331 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;">99</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">4. Practice Excercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>a. Answer Mental Mathematics of Exercises 4.4 (numbers 1-14) on page 334 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>b. Solve Written Mathematics of Exercise 4.3 (numbers 1-10) on page 335-336 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Checking for understanding</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">Solve Written Mathematics of exercises 4.4 (numbers 11-16) on page 337 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">Solve Written Mathematics of Exercise 4.4 (numbers 17-20) on page 337 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">If there is enough time, solve Challenge problems of exercise 4.4 on page 337 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-align: center;">Lesson 4.5</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-align: center;">Kite</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">!. <span> </span>ematical Concepts and Skills</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A kite is a quadrilateral with two distinct pairs of congruent, adjacent sides</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If<span> </span>exactly oone diagonal of a quadrilateral is the perpendicular bisector of the other diagonals are perpendicular.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If a quadrilateral is akite, then its diagonals are perpendicular.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The area of<span> </span>a kite is half the product of thelengths of its diagonals</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Objectives</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Defie a Kite<span> </span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Prove and supply the theorems related to kites</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Values integration</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Being helpful and friendly</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-align: center;">100</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Materials</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Picture of a boy flying a kite</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Manila paper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Marker</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Instructional Strategy</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Procedure</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Session 1</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall the definition of quadrilateral</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Lesson Proper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Show a picture of a boy flying a kite</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Ask whether a kite csan be considered a quadrilateral.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Ask one student to draw a kite</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Ask another student to define a kite based on the figure .</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Guide the students in proving theorems 4-34, 4-25, and 4-26.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practice Excercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt;">Answer Mental Mathematics of exercise 4.5 (numbers 1-10 ) on page 340-341 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;">Solve Written Mathematics of Excercse 4.5 (numbers1-8) on pages 341 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;">Session 2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignments</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall Theorems 4-25 and 4-26</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Follow-up Lesson</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Illustrative Example</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt;">Solve this problem on the board, Find the area of a kite with diagonals 10cm and 16 cm.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practice Excercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt;">Solve Written Mathematics of Exercise 4.5 (numbers 9-11) on page 342 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-align: center;">101</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">`<span> </span>C. Checking for understanding</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: 0.5in;">Solve Written Mathematics of exercise 4.5 ( numbers 12 ) on page 342 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;">Solve written mathematics of exercise 4.5<span> </span>numbers 13-20) o n page 342- 343 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;">If there is enough time, solve the challenge problems of exercise 4.5 on page 343 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-align: center;">102</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Chapter 5 <span> </span></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;">Similarity</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;">Lesson 5.1</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: center;">Ratio and Proportion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Mathematical Concepts and skills</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A ratio is a comparison of two number sby division</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A proportion is a statement of equality between two ratios.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A proportion can be written inyo its equivalent form by using the laws of proportion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The geometric mean of two numbers is the square root of there product</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Segment AC and segment DF are said to be divided proportionally by point b on AC and point D on DF if AB:BC=DE:EF</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Objectives</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Define and simplify the rarios</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Define a proportion and identify its parts</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Define proportional segments</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Define and apply the geometric mean of two numbers</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>State and apply the fundamental laws of proportion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Values Integration</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Resourcefulness</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Materials</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Pictures</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Birthday cards</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Christmas cards</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span> </span>V. Instructional Strategy</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Whole Class Discussion</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-align: center;">103</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Procedure</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in;">Session 1</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Review using linear equations</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Lesson proper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Show pictures of the Parthenon of Greece and the Triumphal Arch of Constantine in<st1:city w:st="on"><st1:place w:st="on">rome</st1:place></st1:city>, which approximates two golden rectangles</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Tell the students about the golden ration and golden rectangle</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Distribute some pictures, birthday cards and old Christmas cards. Ask the students to measure them to to find out if they approximate the golden rectangle</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Tell the students that being resourceful not only of teachers but also for the students</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Define ration and proportion, Write a proportion and identify its parts</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Illustrate the Laws of Proportion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Illustrate Example <span> </span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt;">Use the example on page 351 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt; text-indent: -0.25in;"><span>8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practice Exercise</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 171pt;">Solve Mental Mathematics of exercise 5.1 (numbers 1-10) on page 359 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;">Solve Written MAthenmatics of exercise 5.1 (numbers 1-4) on page 360 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in;">Session 2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall proportional segmentd</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Follow-up Lesson</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Illustrative Example</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt;">Use the illustrative examples on page 352 of the textbook.</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-align: center;">104</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practice Excercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt;">Solve Written /mathematics of exercise 5-1 (numbers 5-8) on page 361 of the textbook</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Checking for understanding</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in;">Solve written Mathematics of exercise 5.1 (numbers 15-22) on page 363 of the textbook .</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-align: center;">Lesson 5.2</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-align: center;">Proportionality Theorems</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-align: center;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.25in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Mathematical Concepts and skills</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If two triangles have two equal altitudes, then the ratio of their areas is equal to the ratio of ther bases.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Two triangles on the same base and between two parallels are equal in area</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If a line is parallel to one side of a triangle and intersects the other two sides in sistinct points, then it divides the two sides proportionally.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>If a line divides two sdes of a triangle proportionally, then the line is parallel to the third side.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.5in;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Objectives</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in;">To prove and apply the proportionality theorem and its converse.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.5in;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Values Integration</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in;">Reliance on one’s ability and judgement</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.5in;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Materials</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in;">Activity sheets</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in;">Rulers</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-align: center;">105</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.5in;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Instructional Strategies</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practical work</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.5in;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Procedure</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in;">Session 1</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary work</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall the are<span> </span>Formula for triangles and theorem 4-5</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Lesson Proper</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2.25in;">Activity 1</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.75in; text-indent: -0.5in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Give each student a photocopy of this activity</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Draw two parallel lines. Name the first line l1 and the second line l2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Plot any two points B and I on l2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Plot any two points E and L on L2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Draw BE, <st1:place w:st="on"><st1:city w:st="on">BL</st1:city>, <st1:state w:st="on">IL</st1:state></st1:place>, and IE.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>e.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>What geometric figures are formed</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>f.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Name two overlapping geometric figures.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>g.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Do they have the same altitudes? Why?</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>h.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Do they have the same base?</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>i.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>What can you say about their areas</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 2in; text-indent: -0.25in;"><span>j.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>What can you conclude?<br />
Activity 2</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Give each student a photocopy of this activity.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 207pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Name the first one l3 and the second l4</div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-85489308783194348512011-03-23T18:32:00.000-07:002011-03-23T18:32:41.568-07:00Chapter 3: Triangle Congruence<div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><b><span style="font-size: 18pt;">CHAPTER </span></b><b><span style="font-size: 14pt;">Triangle Congruence<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><b><span style="font-size: 18pt;"> 3<o:p></o:p></span></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center; text-indent: 0.5in;"><b><span style="font-size: 12.5pt;">Lesson 3.1<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center; text-indent: 0.5in;"><b><u><span style="font-size: 13pt;">Conditions for Triangle Congruence<o:p></o:p></span></u></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center; text-indent: 0.5in;"><span style="font-size: 10pt;">(Textbook pages 204-226, 3 sessions)</span></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-align: center; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -27pt;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b> Mathematical Concepts and Skills<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Two triangles are congruent if their corresponding parts are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Congruence for triangles is <i>reflexive, symmetric, </i>and <i>transitive.</i></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, respectively, then the triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The SSS Postulate, SAS Postulate, ASA Postulate, and the SAA Theorem are used to prove that two triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -63pt;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrate and define congruent triangles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove that congruence for triangles is reflexive, symmetric, and transitive.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Use inductive skills to establish the conditions or correspondence sufficient to guarantee congruence between triangles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Apply deductive skills to show congruence between triangles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -63pt;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -9pt;">The need to be honest and the importance of curiosity.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -27pt;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">bond paper ruler</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Pair of scissors protractor</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -63pt;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.5in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Whole Class Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.5in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practical Work</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -27pt;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b>Session 1<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -9pt;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -9pt;">1.Check the assignment.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -9pt;">2.Recall the definition of congruent triangles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -9pt;">3.Recall Theorem 2-3: Congruence for angles is an equivalence</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Proper<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to draw any triangle. Tell them to cut out their paper triangle and then paste it on two sheets of bond paper.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to compare the two triangles. If they find difficulties comparing the two triangles, tell them to do the following. Tell them also that being curious is very important in mathematics.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: 9pt;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>measure their angles using protractor</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: 0in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>measure their sides using a ruler</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -9pt;">3. Introduce the terms <i>corresponding angles, corresponding sides, and congruent triangles </i>including the symbol “↔” for<i>correspondence.<o:p></o:p></i></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">4. Ask what makes two triangles congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">5. Prove Theorem 3-1.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">6. Tell the students to work with a partner and work on Explore on page 208 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">7. Practice Exercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 93pt;">a. Answer Mental Mathematics of Exercise 3.1 (numbers 1-5) on page 218 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 93pt;">b. Solve Written Mathematics of Exercise 3.1 (numbers 1 and 2) on pages 220-221 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt;"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt;"><b> </b>Solve Written Mathematics of Exercise 3.1 (numbers 3-7) on pages 221-222 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt;"><b>Session 2<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -9pt;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 45pt;">1. Check the assignment.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.5in; text-indent: 45pt;">2. Recall the three Congruence Postulates for Triangles.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -9pt;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrative Examples</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt;">Use the example on page 212 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: 9pt;"> 2. Explain the proof of SAA Theorem.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"> 3. Practice Exercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"> Solve Written Mathematics of Exercise 3.1 (numbers 8-11) on page 223 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -9pt;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><b> </b>Solve Written Mathematics of Exercise 3.1 (numbers 12 and 13) on page 224 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt;"><b>Session 3<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: 0in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: 0in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the SAA Theorem.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrative Examples</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt;">Use the example on page 213 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.5in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;">Solve Written Mathematics of Exercise 3.1 (numbers 14-16) on page 224 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;">Solve Written Mathematics of Exercise 3.1 (numbers 17 and 18) on page 225 of the textbook. Cover your work to be honest.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;">Solve Written Mathematics of Exercise 3.1 (numbers 19 and 20) on page 225 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.5in;"><b><span style="font-size: 12.5pt;">Lesson 3.2<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.5in;"><b><u><span style="font-size: 13pt;">Applying the Conditions for Triangle Congruence</span></u></b><span style="font-size: 13pt;"><o:p></o:p></span></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.5in;"><span style="font-size: 10pt;">(Textbook pages 227-238, 2 sessions)<o:p></o:p></span></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical Concepts and Skills</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The corresponding parts of two triangles can be approved congruent by using the definition of congruent triangles, the congruence postulates for triangles, and the SAA Theorem.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Every angle has exactly one bisector.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 135pt; text-indent: -99pt;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To prove the corresponding parts of two congruent triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To apply the congruence postulates in proving triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b> Values Integration<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;">Tolerance for the feelings, actions, and attitudes of others</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -27pt;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt;">manila paper marker</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: 0.5in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: 0.5in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discovery</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in; text-indent: -0.25in;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b> Procedure</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b>Session 1<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.25in; text-indent: 0.5in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the following:</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">a. SSS Postulate</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">b. SAS Postulate</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">c. ASA Postulate</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in;">d. SAA Postulate</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b>B. Lesson Proper<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><span style="height: 113px; left: 0px; margin-left: 120px; margin-top: 14px; position: absolute; width: 264px; z-index: -1;"><img height="113" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1028" width="264" /></span> 1. Present the following triangles on the board:</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">2. Ask the students to complete the following:</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> AB is congruent to ___</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 117pt; text-indent: -0.25in;">b. BC is congruent to ___</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 189pt; text-indent: -1.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> AC is congruent to ___</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 189pt; text-indent: -1.25in;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> <A is congruent to ___</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 189pt; text-indent: -1.25in;">e.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> <B is congruent to ___</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 189pt; text-indent: -1.25in;">f.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> <C is congruent to ___</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The students should see that when two triangles are congruent their corresponding sides and corresponding angles are also congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Give illustrative examples on how to prove the corresponding parts of congruent triangles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove the Angle Bisector Theorem.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 189pt; text-indent: -1.5in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Answer the Mental Mathematics of Exercise 3.2 (numbers 1-4) on page 232 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 99pt; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Solve Written Mathematics of Exercise 3.2 (numbers 1-3) on page 233 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-indent: 0.75in;"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><b> </b>Solve Written Mathematics of Exercise 3.2 (numbers 4-8) on page 234 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 0.75in;"><b>Session 2<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -9pt;">1. Check the assignment.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.25in; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of angle bisector and the definition of perpendicular.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1.5in; text-indent: -0.5in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrative Example</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"> Use the example on page 231 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;">2. Practice Exercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in;"> Solve Written Mathematics of Exercise 3.2 (numbers 9-12) on page 236 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;">Solve Written Mathematics of Exercise 3.2 (numbers 13-16) on page 236 of the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.5in;">Tell the students to be honest in doing the exercises.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.25in;">Solve Written Mathematics of Exercise 3.2 (numbers 17-20) on 237 for the textbook.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.25in;"><b>If there is enough time, solve the Challenge Problems of Exercise 3.2 on page 238 of the textbook.<o:p></o:p></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.25in;"><br />
</div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.25in;"><b><span style="font-size: 12.5pt;">Lesson 3.3<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.25in;"><b><u><span style="font-size: 13pt;">Congruence and Inequality Properties in an Isosceles Triangle</span></u></b><span style="font-size: 13pt;"><o:p></o:p></span></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-align: center; text-indent: 0.25in;"><span style="font-size: 10pt;">(Textbook pages 239-252, 3 sessions)<o:p></o:p></span></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 1in; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 45pt; text-indent: -0.25in;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical Concepts and Skills<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two sides of a triangle are congruent, then the angles opposite these sides.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Every equilateral triangle is equiangular.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Each angle of an equilateral triangle has a measure of 60°.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two angles of a triangle are congruent, then the sides opposite these angles are congruent.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Every equiangular triangle is equilateral.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If one side of the triangle is longer than the second side, then the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If one angle of the triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two sides of a triangle are congruent to two sides of a second triangle and the included angle of the first triangle has a greater measure than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two sides of one triangle are congruent to two sides of a second triangle and the included angle of the first triangle has a greater measure than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: -0.5in;"><b>II. Objectives<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: 0in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove and apply the Isosceles Triangle Theorem and its converse.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: 0in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove that every equilateral triangle is equiangular.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: 0in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove that every equiangular triangle is equilateral.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: 0in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove that every angle of an equilateral has a measure of 60°.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove that if one side of a triangle is longer than a second side, then the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove that if one angle of a triangle is longer than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 63pt; text-indent: 0in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove and apply the Hinge Theorem and its converse.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"><b>III. Values Integration<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"><b> </b>The importance of joint effort in accomplishing a given task</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"><b>IV. Materials</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"> ruler protractor straws</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"><b>V. Instructional Strategies</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"> A. Discussion</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"> B. Group Work</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"> C. Practical Work in Small Groups</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"><b>VI. Procedure</b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 27pt;"> <b>Session 1<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 66pt; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 102pt; text-indent: -39pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 102pt; text-indent: -39pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of isosceles triangle.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 66pt; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Proper<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Remind the students about the importance of joint effort in accomplishing a given task and then tell them to do the following activity in pairs.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">a. Draw an isosceles triangle <i>ABC</i> with base <i>BC</i>.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">b. Using a protractor and a ruler, bisect the vertex angle <i>BAC</i>.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">c. Let the bisector intersect <i>BC</i> at point <i>D.</i></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt;">d. With a protractor measure <<i>BAD </i>and <<i>CAD</i>.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">2. Ask the following questions:</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"> a. Why are <<i>BAD </i>and <<i>CAD </i> congruent?<br />
b. Is side <i>AB</i> congruent to side <i>AC</i>? Why?<br />
c. Is side <i>AD</i> congruent to itself? Why?</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"> d. Can you now conclude that ∆<i>BAD</i> is congruent to ∆<i>CAD</i>? Why?</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"> e. Is <<i>B</i> congruent to <<i>C</i>? Why?</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">3. Explain the proof of the Isosceles Triangle Theorem and Theorem 3-5.</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;">4. Practice Exercises</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"> a. Answer Mental Mathematics of Exercise 3.3 (numbers 1-5) on page 246 of the textbook.</div><div class="MsoNormal" style="color: #222222; line-height: 18px; margin-left: 81pt; text-indent: -0.25in;"><span class="Apple-style-span" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"> b. Solve Written Mathematics of Exercise 3.3 (numbers 1 and 2) on pages 247-248 of the textbook.</span><br />
<div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">C. Assignment<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>Solve Written Mathematics of Exercise 3.3 (numbers 3 and 4) on page 249 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 2<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the Angle Addition Postulate, Theorem 2-10, and Theorem 2-11.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Divide the students in small groups. Tell them to do the following activities.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Activity 1<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Draw a scalene triangle.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Measure each side of the triangle in centimetres.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Label the longest side AB<i> </i>and the shortest side BC<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Measure the angle opposite to AB and the angle opposite AC. Compare their measurements<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>e.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Measure the angle opposite to BC. Compare its measure with the measure of the angle opposite AB.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>f.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Compare the measurement to the angle opposite AC with the measure of the angle opposite BC.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>g.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">What can you conclude?<b><o:p></o:p></b></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Activity 2<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Draw a scalene triangle.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Label the angle which seems to have the largest measure A, and the angle which seems to have the smallest measure B.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Measure each angle and the side opposite each angle.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 1in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">What can you conclude?<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Complete the proof of the Angle Side Inequality Theorem.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Explain the proof of Theorem 3-6: The Side Angle Inequality Theorem.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Illustrative Example<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Use the examples on page 244 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-left: 0.75in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.3 (number 5) on page 249 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Checking for Understanding<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.3 (numbers 11-16) on the page 250 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment</span></b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.3 (numbers 17-20) on page 251.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If there is enough time, solve the Challenge Problems of Exercise 3.3 on page 252 of the textbook.<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson 3.4<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Overlapping Triangles<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">(textbook pages 253-261, 1 session)<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A geometric figure may be made up of two or more overlapping triangles.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">To prove overlapping triangles, it is better to mentally separate or redraw into separate figures.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Objective<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">To prove that overlapping triangles are congruent<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Values Integration<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">The value of hard-work<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Materials<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Wires<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Rulers<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Instructional Strategies<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practical Work<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Discussion<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Procedure<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the Three Congruence Postulate for Triangles.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson Proper<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Using wires, make two congruent triangles.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><br />
<span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><br />
Let two triangles overlap.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><tbody>
<tr><td height="23" width="196"></td></tr>
<tr><td></td><td><br />
</td></tr>
</tbody></table><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><o:p> </o:p></span><br />
<div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><br clear="ALL" /><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">After doing the activity, ask the students whether they find it easy to make two congruent triangles using wires. Tell them t hat life is not always a bed of roses. One must work hard to succeed in life.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><br />
<span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><br />
Write a problem using a figure similar to the overlapping triangles made of wires.<span> </span><span> </span><b>A<span> </span><span> </span>D</b><o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Given:<span> </span>AB ≈ DC<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><span> </span>AC ≈ DB<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove: ΔABC ≈ ΔDCB<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><b>B<span> </span><span> </span>C<o:p></o:p></b></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">4.<span> </span>Tell the students to redraw the overlapping triangles into separate<span> </span>figure. Then ask them to write a proof.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">5. Practice Exercise<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>a. Answer the Mental Mathematics of Exercise 3.4 (numbers 1-4)<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>on page 255 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>b. Solve Written Mathematics of Exercise 3.4 (numbers 1-4) on<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>on pages 256-257<o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Checking for Understanding<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.4 (numbers 5-8) on page 258 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.4 (numbers 9-13) on page 259 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div align="center" class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson 3.5<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Right Triangle Congruence and Problems Involving Altitudes and Medians<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-align: center;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">(Textbook pages 262-275, 3 sessions)<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If two legs of a right triangle are congruent to the corresponding leg of another right triangle, then two triangles are congruent.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If one leg and one acute angle of a right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the two right triangles are congruent.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If the hypotenuse and one leg of a right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the two right triangles are congruent.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If the hypotenuse and one acute angle of a right triangle mare congruent to the corresponding hypotenuse and acute angle of another right triangle, then the two right triangles are congruent.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Identify the parts of a right triangle<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove and apply the following theorems:<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Leg-Leg Congruence Theorem<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Leg-Acute Angle Congruence Theorem<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Hypotenuse-Leg Congruence Theorem<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Hypotenuse-Acute Angle Congruence Theorem<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve problems involving altitudes and medians<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Values Integration<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">The need to act with prudence<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Materials<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Manila paper<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Marker<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Instructional Strategy<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Discussion<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Procedure<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 1<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the SAS Postulate.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson Proper<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Draw a right triangle on a manila paper. Post the manila paper on the board. Ask one student to identify its parts.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Ask the students to enumerate all the postulates, definitions, and theorems that can be used to prove that two triangles are congruent.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Guide the students in proving the Leg-Leg Congruence Theorem and the Hypotenuse-Leg Congruence Theorem.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove the Leg-Acute Angle Congruence Theorem and the Hypotenuse-Acute Angle Congruence Theorem. Tell the students that they should be careful in writing the proof to avoid erroneous steps and reasons. Even in life, it is always better to act with prudence.<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.5 (numbers 1-5) on page 272 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><b>Session 2<o:p></o:p></b></span></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the Isosceles Triangle Theorem, the SAS, ASA, SSS Postulates, and the SAA Theorem.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Illustrative Examples<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Use the examples on page 263 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Answer the Mental Mathematics of Exercise 3.5 (numbers 1-6) on page 271 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.5 (numbers 1-5) on page 272 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.5 (numbers 6-4) on page 273 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 3<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the definition of altitude and definition of median.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Illustrative Examples<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Use the example on page 268 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.5 (numbers 10-13) on page 274 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Checking for Understanding<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.5 (numbers 14-15) on page 274 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.5 (numbers 16-18) on page 275 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If there is enough time, solve the Challenge Problems of Exercise 3.5 on page 275 of the textbook.<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson 3.6<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Theorems Related to Bisectors and Perpendicular Lines<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">(Textbook pages 276-288, 2 sessions)<o:p></o:p></span></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">The distance from a point to a line is the length of the perpendicular segment from the point of the line.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A point on the bisector of an angle is equidistant from the sides of the angle.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A point equidistant from the sides of an angle lies on the bisector of an angle.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A point on the perpendicular bisector of a segment is equidistant from the endpoint of a segment.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A point equidistant from the endpoint of a segment lies on the perpendicular bisector of the segment.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If a line contains two points each of which is equidistant from the endpoints of a segment, then the line is the perpendicular bisector of the segment.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">On a plane through a given point on a line, there is exactly one line perpendicular to the line.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">There is one and only one line perpendicular to a given line from an external point.<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Define the distance from a point to a line<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove and apply the theorems about bisectors and perpendicular lines<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Value Integration<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practicality<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Materials<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Coin<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Ruler or tape measure<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Instructional Strategies<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Whole Class Discussion<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practical Work<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Procedure<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 1<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the Assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the definition of perpendicular<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson Proper<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Put a coin on the floor. Have one student measure the distance from one coin to one of the walls of the room.<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Draw a line and external point on the board. Ask one student to determine the distant from the point to the line.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span class="Apple-style-span" style="font-family: Arial, sans-serif; font-size: 16px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><br clear="ALL" /><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><br />
<span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><br />
Ask another student to draw a perpendicular segment from the external point to the line. Then tell the student to measure the length of the segment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><tbody>
<tr><td height="15" width="203"></td></tr>
<tr><td></td><td><br />
</td></tr>
</tbody></table><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><o:p> </o:p></span><br />
<div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><br clear="ALL" /><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Ask whether the length of the segment is equal to the distance from the external point to the line.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Ask the students to define the distance from an external point to the line. Ask them to relate the activity to something they have done before. Did they use their past experiences in doing the task? Ask them the importance of practicality in life.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Discuss the proof of Theorem 3-14 and Theorem 3-16<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercise<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove Theorem 3-15<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Study the proof of Theorem 3-17, Corollary 3-17.1, and Theorem 3-18<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove Theorem 3-19<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-indent: 0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 2<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the definition of a linear pair and the Linear Pair Postulate<b><o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove Theorem 3-17, Corollary 3-17.1, and Theorem 3-18<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Illustrative Example<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Explain the proof of this problem.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Given: AD ┴ bisector of BC<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove: ΔABC is isosceles<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><span> </span><b><span> </span>A<o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px;"><tbody>
<tr><td height="0" width="180"></td></tr>
<tr><td></td><td><img height="88" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image011.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1038 _x0000_s1039 _x0000_s1040" width="111" /></td></tr>
</tbody></table><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><o:p> </o:p></span><br />
<div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><br clear="ALL" /><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><span> </span><b>B <span> </span>D<span> </span>C<o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Answer Mental Mathematics of Exercise 3.6 (numbers 1-5) on page 284 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.6 (number 1-6) on page 285 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Checking for Understanding<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 3.6 (numbers 7-10) on page 286-287 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If there is enough time, solve the Challenge Problems of Exercise 3.6 on pages 288 of the textbook.<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson 4.1<o:p></o:p></span></b></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Types of Quadrilaterals and their Properties<o:p></o:p></span></div><div align="center" class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-align: center;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">(Textbook pages 296-307, 3 sessions)<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A diagonal of a parallelogram forms two congruent triangles.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">In a parallelogram, any two opposite angles are congruent<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">In a parallelogram, any two consecutive angles are supplementary<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">In a parallelogram, any two opposite sides are congruent<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">The diagonals of a parallelogram bisect each other<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If two lines are parallel, then all points of each line are equidistant from the other line.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">II. <span> </span>Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall previous knowledge on the different types of quadrilaterals<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Apply inductive and deductive skills to derive the properties of a parallelogram<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Apply the theorems about the properties of parallelograms<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">III. Values Integration<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>Carefulness in accomplishing a task<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">IV. Materials<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>geoboard<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>rubber bands<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">V.<span> </span>Instructional Strategies<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>A. Practical Work<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>B. Discussion<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">VI. Procedure<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>Session 1<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Acqtivities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the Assignment<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the types of quadrilaterals<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson Proper<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Tell the students to do the following activity. Remind the students to be always careful in doing their task<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Using a geoboard and rubber bands, make quadrilaterals with the following descriptions:<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Symbol; font-size: 12pt; line-height: 18px;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A quadrilateral in which both pairs of opposite sides are parallel<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Symbol; font-size: 12pt; line-height: 18px;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A parallelogram with four right angles<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Symbol; font-size: 12pt; line-height: 18px;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A parallelogram with four congruent sides<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Symbol; font-size: 12pt; line-height: 18px;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A rectangle with four congruent sides<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Symbol; font-size: 12pt; line-height: 18px;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A quadrilateral with exactly one pair of parallel sides<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Each time you are finished making one of the quadrilaterals, ask your seatmate these questions: “What type of quadrilateral is on my geoboard? Why?”<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Ask the students to work on Explore on pages 297-298 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Discuss the proofs of Theorems 4-1, 4-2, 4-3. 4-4. And 4-5<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Answer Mental Mathematics of Exercise 4.1 (numbers 1-6) on page 303 of the textbook<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove Corollary 4-1.1<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 4.1 (numbers 1-4) on page 304 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.5in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 2 <span> </span><o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall the Systems of Linear Equations<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Illustrative Examples<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Explain the proof of this problem<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Given: Quadrilateral ABCD is a parallelogram<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">1 ≈ </span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">2<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove: </span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">3 ≈ 4</span><span class="Apple-style-span" style="font-family: Arial, sans-serif; font-size: 16px;"> </span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 4.1 (numbers 5-7) on page 304 of the textbook<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Assignment<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 4.1 (numbers 8-10) on page 305 of the textbook.<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; text-indent: 0.5in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Session 3<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Preliminary Activities<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Check the assignment.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Recall Theorems 4-1 to 4-5<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Illustrative Examples<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Given: Quadrilateral CDEF is a parallelogram<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span>FH = DH<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Prove: Δ GDE ≈ ΔHOC<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span class="Apple-style-span" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><br />
</span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; height: 74px; left: 0px; margin-left: 131px; margin-top: 7px; position: absolute; width: 202px; z-index: 251678720;"><span class="Apple-style-span" style="font-family: Arial, sans-serif; font-size: 16px;"><span><br />
</span></span></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Practice Exercises<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 4.1 (numbers 11-13) page 305 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span></b><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Checking for Understanding<span> </span><o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Solve Written Mathematics of Exercise 4.1 (numbers 16 and 17) on page 306 of the textbook.<o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">If there is enough time, solve Challenge Problems of Exercise 4.1 on page 307 of the textbook.<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div align="center" class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Lesson 4.2<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Properties of the Diagonals of Special Quadrilaterals<o:p></o:p></span></b></div><div align="center" class="MsoListParagraphCxSpMiddle" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-align: center;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">(</span></b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Textbook pages 308-314, 2 sessions)<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">I. Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">A. The diagonals of a rectangle are congruent<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">B. The diagonals of a square bisect the vertex angle<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">C. The diagonals of a rhombus are perpendicular<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">D. Each diagonal of a rhombus, bisects the opposite angles of the rhombus<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">E. If a parallelogram has at least one right angle, then it is a rectangle<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">F. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><br />
</div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">II. Objectives<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Apply inductive and deductive skills to derive the additional properties of rectangles, rhombi, and squares.<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">Apply the Theorems about rhombi, rectangles and squares<o:p></o:p></span></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><b><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;">III. Values Integration<o:p></o:p></span></b></div><div class="MsoNormal" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; margin-bottom: 0in;"><span lang="EN-PH" style="font-family: Arial, sans-serif; font-size: 12pt; line-height: 18px;"><span> </span><span> </span>The importance of cooperation in accomplishing a task.</span></div></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-11183756300898683182011-03-23T18:28:00.000-07:002011-03-23T18:33:35.324-07:00Chapter 2: Geometric Relations<div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-size: 24pt; line-height: 36px;"><br />
</span></b><b><span style="font-family: Arial; font-size: 24pt; line-height: 36px;">Chapter </span></b><b><i><span style="font-family: Arial; font-size: 20pt; line-height: 31px;">Geometric Relations</span></i></b><b><i><span style="font-family: Arial; font-size: 24pt; line-height: 36px;"><o:p></o:p></span></i></b></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div class="MsoNormal" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><b><span style="font-family: Arial; font-size: 24pt; line-height: 36px;"> 2<o:p></o:p></span></b></div></div><div align="center" class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; text-align: center;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Lesson 2.1<o:p></o:p></span></b></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; padding-bottom: 1pt; padding-left: 0in; padding-right: 0in; padding-top: 0in;"><div align="center" class="MsoNormal" style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0in; padding-top: 0in; text-align: center;"><b><i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Relations Involving Segments an Angles<o:p></o:p></span></i></b></div></div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in;"><span style="height: 311px; left: 0px; margin-left: 298px; margin-top: 13px; position: absolute; width: 546px; z-index: -16;"><img alt="absol.jpg" height="311" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image002.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="Picture_x0020_0" width="546" /></span><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">I. Mathematical Concecpts and Skills<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">The <i>absolute value</i> of <i>x</i> denoted by is nonnegative, and is the opposite of <i>x</i> if <i>x</i> is negative.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 316px; left: 0px; margin-left: 307px; margin-top: 34px; position: absolute; width: 583px; z-index: -13;"><img height="316" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image004.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1029" width="583" /></span><span style="height: 368px; left: 0px; margin-left: 142px; margin-top: 45px; position: absolute; width: 647px; z-index: -15;"><img height="368" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image006.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1027" width="647" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">There is a one-to-one correspondence between the points of a line and the set of real numbers such that the distance between any two points of the line is the aabsolute value of the difference between the corresponding numbers.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 411px; left: 0px; margin-left: 514px; margin-top: 0px; position: absolute; width: 722px; z-index: -14;"><img height="411" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image007.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1028" width="722" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Segment is congruent to segment if and only if the length of line <i>AB</i> is equal to the length line <i>CD</i> .<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">M</span></i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> is the midpoint of line <i>AB </i>if and only if (a) <i>M</i> lies between <i>A and B</i>and (b)<i> AM = MB</i>.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Given two points P and S on a line, a coordinate system can be chosen in such a way that the coordinate of P is 0 and the coordinate of S is greater than ).<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">On a ray AB, there is exactly one point P that lies at a distance x from<br />
A.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 355px; left: 0px; margin-left: 570px; margin-top: 15px; position: absolute; width: 624px; z-index: -12;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image009.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1030" width="624" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Every segment has exactly one midpoint.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ray <i>ET</i> is the bisector of <i><BEH</i> if and only if <i>T </i>is in the interior of<i><BEH </i>and<i> <</i></span><st1:stockticker><i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">BET</span></i></st1:stockticker><i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> <</span></i><st1:stockticker><i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">HET</span></i></st1:stockticker><i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">.</span></i><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Congruence for angles is reflexive, symmetric, and transitive.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Objectives<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To find the coordinate of a point on a number line<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To find the distance between two points in a number line<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To solve equations involving absolute values<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To find the coordinate of the midpoints of a segment<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To plan and write two-column proofs<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To apply the properties of equalities in proving<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To apply the definition of angle bisector in computations<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To prove the congruence for angles is reflexive, symmetric, and transitive<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Values Integration<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Being open and honest<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Materials<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">ruler<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">sticks<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Instructional Strategy<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Discussion<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Procedure<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Session 1<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignment.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Recall the definition of between and the definition of collinear points.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Lesson Proper<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Draw a line on the board and ask the students to describe it. Tell the students that to each of the point on the number line there corresponds a real number and to every real number there corresponds a point on the number line.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="height: 363px; left: 0px; margin-left: 223px; margin-top: 1px; position: absolute; width: 766px; z-index: -11;"><img height="363" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image011.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1031" width="766" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students to give examples of real numbers between any two numbers. Tell them to plot their corresponding points on the same number line.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students to define absolute value. Then tell them to do the following exercises.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">l-6l b. l-8l+l-3l<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">–l-6l+l+8l e. -4l-8-(-3)+1l<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">-6-l-10l<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 371px; left: 0px; margin-left: 218px; margin-top: 18px; position: absolute; width: 703px; z-index: -10;"><img height="371" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image013.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1032" width="703" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students to find the number of units from 5 to -2 on the number line by counting the number of units from -2 to 5.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Illustrate how to use the concept of absolute value in finding the distance between two points on a number line.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Illustrate the meaning of congruent segments by asking the students to measure two sticks with equal lengths. Next, draw a line similar to the one below.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="height: 355px; left: 0px; margin-left: 218px; margin-top: 0px; position: absolute; width: 824px; z-index: -9;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image015.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1033" width="824" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 355px; left: 0px; margin-left: 223px; margin-top: 9px; position: absolute; width: 801px; z-index: -8;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image017.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1034" width="801" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Draw this number line on the board.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the following questions.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Are points A, M, and B collinear? Why?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Which point is between A and B?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the distance from B to M? from M to A?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">d.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the midpoint of segment AB?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">e.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">When is a point the midpoint of a segment?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Practice Exercises<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Answer Mental Mathematics of Exercise 2.1 (numbers 1-10) on page 116 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.1 (numbers 1-6) on page 116 of the textbook. Tell the students to be honest. They should refrain from looking at their seatmates’ paper.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Assignment<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.1(numbers 7-12) on page 117 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> Session 2<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignment.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Review the past lesson.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 355px; left: 0px; margin-left: 194px; margin-top: 30px; position: absolute; width: 776px; z-index: -7;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image019.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1035" width="776" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Draw the same number line used in Session 1 on the board. The time replace the coordinate of the midpoint by x and ask the following questions:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the distance from B to M? from M to A?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Are the two distances equal ? Why?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Write an equation and solve for x. What is the coordinate of the midpoint?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Show that Postulate 11 can be used as an alternative method in determining the distance between two points.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Prove Theorem 2-1 and Theorem 2-2 on paragraph form.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Practice Exercises<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.1 (numbers 13 and 14) on page 117 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Assignment<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.1 (numbers 15 and 16) on page 118 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> Session 3<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignment.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Recall proving statements in paragraph form.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Follow-up Questions<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Write several number sentences on the board. Ask the students to write opposite each sentence the property of equality being illustrated.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="height: 355px; left: 0px; margin-left: 181px; margin-top: 13px; position: absolute; width: 801px; z-index: -6;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image021.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1036" width="801" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Present the following illustrations.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Tell the students to observe the angles and ask the following questions.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What do you observe?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Is point T in the interior of each angle?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Is it correct to say that m<</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">BET</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> + m<</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">HET</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> = m<BEH?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Present the following illustration:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="height: 355px; left: 0px; margin-left: 163px; margin-top: 17px; position: absolute; width: 778px; z-index: -5;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image023.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1037" width="778" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the following questions:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Is the point S in the interior of <ABC?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Is m<ABC = m<</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">ABS</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> + m<CBS?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Tell the students that ray ET is an angles bisector whereas ray BS is not. Ask the students to define an angle bisector in their own proofs.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Discuss the steps in writing a two-column proof. Then prove Theorem 2-3.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Practice Exercise<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.1 (number 17) on page 118 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Assignment<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.1 (number 19) on page 118 of the textbook.<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: justify;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">____________________________________________________________________________________<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: justify;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">Lesson 2.2<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">Adjacent and Conplementary Angles<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">____________________________________________________________________<o:p></o:p></span></div><div align="center" class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">(Textbook pages 119-128, 2 sessions)<o:p></o:p></span></div><div align="center" class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Mathematical Concepts and skills<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Adjacent angles are two angles which have a common vertex and a common side but have no interior point in common.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Angles are complementary if the sum of their measures is 90. Each angles is called a complement of the other.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Of two angles are complementary of congruent angle, then the two angles are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">If two angles are complementary to the same angles, then they are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> II. Objectives<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To illustrate, identify, and define adjacent and complementary angles.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To find the measures of the complements of given angles<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To state, prove, and apply the following:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Theorem2-4.If two angles are complements of congruent angles, then the tow angles are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Corollary 2-4.1 If two angles are complementary to the same angle, then they are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To differentiate a corollary from a postulate.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> </span></b><st1:stockticker><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">III</span></b></st1:stockticker><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">. Values Integration</span></b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> Being friendly to other people<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> <b>IV. Materials</b><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> manila paper<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">marker<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> V.Instuctional Strategy<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> </span></b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Discussion<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> VI.Procedure<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.25in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> Session 1<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignments.<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Recall the meaning of postulate and the properties of equalities.<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Lesson Proper<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Introduce the terms adjacent angles and complementary angles by doing the following activity.<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Draw the following angles on the manila paper. Post the manila paper on the board.<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="height: 355px; left: 0px; margin-left: 163px; margin-top: 9px; position: absolute; width: 879px; z-index: -4;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image025.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1038" width="879" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the following questions:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 164.25pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Symbol; font-size: 10pt; line-height: 14px;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the common vertex of <ABD and <</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">CBD</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">?<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 164.25pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Symbol; font-size: 10pt; line-height: 14px;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the common side of <ABD and <</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">CBD</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">?<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 164.25pt; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Symbol; font-size: 10pt; line-height: 14px;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Do they have common interior points?<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Draw this figure on manila paper. Post the manila paper on the board.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="height: 355px; left: 0px; margin-left: 195px; margin-top: 14px; position: absolute; width: 715px; z-index: -3;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image027.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1039" width="715" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the following questions:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Symbol; font-size: 10pt; line-height: 14px;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the common vertex of <EFG and <EFH?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Symbol; font-size: 10pt; line-height: 14px;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Do <EFG and <EEEFH have a common side?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Symbol; font-size: 10pt; line-height: 14px;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Do they have interior points in common?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students to define in their own words the terms adjacent and complementary angles.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Explain the proof of Theorem 2-4.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students to complete the proof of Corollary 2-4.1 Direct the students’ attention to the proof of this corollary on page 122 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Practice Exercises<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Answer Mental Mathematics of Exercise 2.2 (numbers 1-4) on page 124 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.2 (numbers 1-4 of the textbook in page 125.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Assignment<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve the Written Mathematics of Exercise 2.2 (numbers5-10) on page 126 of the textbook)<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Session 2<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignment.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Review the past lesson.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Follow-up Lesson<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Illustrative Example<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Explain the proof of this problem.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Given <BAD (congruent) <</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">CAE</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Prove: <</span><st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">BAE</span></st1:stockticker><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> (congruent) <CAD<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><span style="height: 355px; left: 0px; margin-left: 178px; margin-top: 15px; position: absolute; width: 720px; z-index: -2;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image029.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1040" width="720" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Practice Exercises<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: 0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.2 (numbers 11 and 12) on page 127 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Checking for Understanding<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.2 (numbers 13-16) on page 127 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Assignment<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> Solve Written Mathematics of Exercise 2.2 (numbers 17-20) on page 127 of the textbook.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">If there is enough time, solve the challenge Problems of Exercise 2.2 on page 118 of the textbook.<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">______________________________________________________________________<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">Lesson 2.3<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><b><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">Supplementary Angles<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 12pt; line-height: 18px;">______________________________________________________________________<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">(Textbook pages 129-139, 2 sessions)<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">J.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Mathematical Concepts and Skills<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Two angles are supplementary if the sum of their measures is 180.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">If two angle are supplements of congruent angles, then the two angles are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">If two angles are supplementary to the same angle, then the two angles are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">If two angles are both congruent and supplementary, then each is a right angle.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> II. Objectives</span></b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To illustrate, identify, and define supplementary angles<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">To state, prove, and apply the following theorems:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Theorem 2-5.If two angles are supplement of congruent angles then the two angles are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Corollary2-5.1 If two angles are supplementary to the same angle, then the two angles are congruent.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Theorem 2-6. If two angles are both congruent and supplementary then each is a right angle.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> </span><st1:stockticker><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">III</span></b></st1:stockticker><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">. Values Integration<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> </span></b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Being helpful<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> <b>IV. Materials<o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> </span></b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">manila paper<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; text-indent: 0.5in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">marker<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">V.Instructional Strategies<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> </span></b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A. Group work<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"> B. Discussion<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">VI. Procedure<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 0.75in; margin-right: 0in; margin-top: 0in; text-indent: 0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Session 1<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignments<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Recall the definitions. of congruent angles and right angles,<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Lesson Proper<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Draw the figures:<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="height: 355px; left: 0px; margin-left: 170px; margin-top: 6px; position: absolute; width: 760px; z-index: -1;"><img height="355" src="file:///C:/DOCUME~1/PHNAVA~1/LOCALS~1/Temp/msohtml1/04/clip_image031.jpg" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1041" width="760" /></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">What is the sum of the two angles in figure 1? in figure 2?<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.75in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Compare the two angles on Figure 1 with those on figure 2.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">After telling the students that the two angles in each figure are supplementary angles, ask them to define supplementary angles in their own words.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students to compare supplementary angles with adjacent angles and with complementary angles.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Ask the students whether the common side of supplementary, and at the same time adjacent angles, is always in the same plane as the other two sides. Ask them to state the theorem or postulate that can be the reason for their answer.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Explain the proof of Theorem 2-5.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Divide the class into small groups. Tell the groups to complete the proof Corollary 2-5.1 and Theorem 2-6. Tell the members of each group to help each other in completing the proof.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Practice Exercise<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Answer the Mental Mathematics of Exercise 2.3 (numbers 1-10) on pages 134-135.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Assignment<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Solve Written Mathematics of Exercise 2.3 (numbers 1-4) of the textbook 134-135.<o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.5in; margin-right: 0in; margin-top: 0in;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; text-indent: 0.5in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Session 2<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 1.25in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Preliminary Activities<o:p></o:p></span></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Check the assignments.<b><o:p></o:p></b></span></div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; margin-bottom: 0in; margin-left: 2in; margin-right: 0in; margin-top: 0in; text-indent: -0.25in;"><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span style="font-family: Arial; font-size: 10pt; line-height: 14px;">Review the past lesson.<b><o:p></o:p></b></span><br />
<span style="font-size: 10pt; line-height: 14px;"></span><br />
<div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B. Follow-up Lesson<o:p></o:p></span></b></span></div><span style="font-size: 10pt; line-height: 14px;"></span><br />
<div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Illustrative Example<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Explain the proof of this problem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Given: ABD is supplementary to DBE.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> CBE is supplementary to DBE.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Prove: ABD is congruent to CBE<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> 2. Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Solve Written Mathematics of Exercise 2.3 (numbers 5-8) on page 136 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C. Checking for Understanding<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.3 (numbers 9-11) on page 137 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D. Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.3 (numbers 12-15) on page 138 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <b>If there is enough time, solve the Challenge Problems of Exercise 2.3 on page 139 of the textbook.<o:p></o:p></b></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Lesson 2.4<o:p></o:p></span></b></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><i><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Linear Pairs</span></i></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><o:p></o:p></span></b></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">(Textbook pages 140-146, 2 sessions)<o:p></o:p></span></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Mathematical Concepts and Skills<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Two angles form a linear pair if and if only if they are adjacent angles and their uncommon sides are opposite rays.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">If two angles form a linear pair, then they are supplementary angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Objectives<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To illustrate, identify, and define a linear pair<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To state and apply the Linear Pair Postulate<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Values Integration<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Refine civic consciousness to the definition of adjacent angles<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Procedure<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">manila paper<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">markers<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Instructional Strategies<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Individualized Instructions<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Discussion<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Procedure<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Session 1<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall the definition of adjacent angles and opposite rays.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Lesson Proper<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Present the following pairs of angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2. Ask the students to compare the angles in the figure 1 with those in figure 2.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3. Tell the students that the two angles in the first figure from a linear pair.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4. Ask the students to define a linear pair in their own words.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">5. Present at least three figures on the board that form a linear pair.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">6. Ask the students to complete this statement, “If two angles form a linear pair, then __________________.”<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">7. Illustrate how to solve this problem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> If two angles are a linear pair and the measure of one is four times the measure of the other, what is the measure of each angle?<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">8. Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: 0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a. Answer Mental Mathematics of Exercises 2.4 (numbers 1-3) on page 141 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: 0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b. Solve Written Mathematics of Exercise 2.4 (numbers 1-4) on page 142 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <b>C. Assignment<o:p></o:p></b></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Solve Written Mathematics of Exercise 2.4 (numbers 5-10) on page 142 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Session 2<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> A. Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Illustrative Example<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> 2. Review the past lesson.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <b>B. Follow-up Lesson<o:p></o:p></b></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Illustrative Example<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Explain the proof of this problem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Given: <1 and <2 form a linear pair.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <4 and <3 form a linear pair.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Prove: <1 is congruent to <4<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> 2. Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Solve Written Mathematics of Exercise 2.4 (numbers 11-13) on page 143 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.5in; text-indent: 0in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Checking for Understanding<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.4 (numbers 14 and 15) of the textbook on pages 144-145.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 48pt; text-indent: -12pt;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.4 (number 16 and 17) on page 145 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">If there is enough time, solve the Challenge Problems of Exercise 2.4 on page 146 of the textbook.<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Lesson 2.5<o:p></o:p></span></b></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><i><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Vertical Angles<o:p></o:p></span></i></b></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">(Textbook pages 147-151, 2 sessions)<o:p></o:p></span></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Mathematical Concepts<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Two angles are vertical angles if and if only if they are nonadjacent angles formed by two intersecting lines.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Vertical angles are congruent.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Objectives<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To illustrate, identify, and define vertical angles<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To state, prove, and apply the Vertical Angle Theorem<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Values Integration<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Being open and honest<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Materials<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">manila paper<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">marker<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">protractor<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Instructional Strategy<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Discussion<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Procedure<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Session 1<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall the definition of adjacent angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Lesson Proper<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Introduce the concept of vertical angles by drawing two intersecting lines on manila paper. Post the manila paper on the board.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask one student to measure the angles using a protractor.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the students to make a general statement.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Guide the students in proving the Vertical Angle Theorem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 114pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Practice Exercises.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 2in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.5 (numbers 1-6) on page 149 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.5 (number 7-10) on page 150 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Session 2<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall the definition of perpendicular bisector of a segment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Follow-up Lesson<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Illustrative Example<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Explain the proof of this problem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Given: m BET =60<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> M HET =30<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> MA MR<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Prove: BEH is congruent to AMR<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 2.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Answer Mental Mathematics of Exercise 2.6 (numbers 1-4) on page 156 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 2.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.6 (numbers 8-10) on page 158 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Checking for Understanding<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.6 (number 11) of the textbook on page 158 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.6 (number 12-20) on page 158- 160 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> If there is enough time, solve the Challenge Problems on page 160 of the textbook.<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Lesson 2.7<o:p></o:p></span></b></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><i><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Angles and Sides of a Triangle<o:p></o:p></span></i></b></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">(Textbook pages 161-174, 5 sessions)<o:p></o:p></span></span></div><div align="center" class="MsoNormal" style="font-family: Arial; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Mathematical Concepts and Skills<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">An exterior angle is an angle l, which is adjacent and supplementary to one of the angles of a triangle.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Remote interior angles are which are not adjacent to the given exterior angle of the triangle.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">An adjacent interior angle is an interior angle, which forms a linear pair with the given exterior angle of a triangle.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">The measure of an exterior angle is equal to the sum of its remote interior angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">AB > CD if and if only if AB > CD.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">AB < CD if and if only if AB < CD.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> A > B if and if only if m A > m B.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> A < B if and if only if m A < m B.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">The whole is greater than any of its parts.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">J.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">The measure of an exterior of a triangle is greater than the measure of either of the two remote interior angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">K.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">In any triangle, the sum of the lengths of any two sides is greater than the length of the third side.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">L.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Objectives<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To illustrate, identify, and define exterior angles, remote interior angles, adjacent interior angles, greater than segments and angles, and less than for segments and angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To state and apply the properties of inequalities.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To prove and apply the theorems about exterior angles of a triangle.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To prove and apply the theorem, which says that, "The whole is greater than any of its parts"<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To show that in any triangle, the sum of the lengths of any two sides is greater than the length of the third side<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To apply the Triangle Inequality Theorem in computations<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To prove and apply the Pythagorean Theorem<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Values Integration<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Concern for others<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Materials<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">manila paper<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">marker<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">cutouts<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Instructional Strategies<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Discussion<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Group Work<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Procedure<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Session 1<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall the definition of a triangle.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Lesson Proper<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Draw a triangle like the one below:<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 99pt;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 99pt;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 99pt;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 99pt;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 99pt;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Use the figure, guide the students in identifying and defining exterior angles and remote interior angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Guide the students in defining less than for segments, greater than for segments, less than for angles and greater than for angles.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Illustrate the properties of inequalities. Give at least two examples of each property.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Explain the proof pf Theorem 2-9.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Illustrative Example<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Use the example on page 162 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 2in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (numbers 1-3) on page 172 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (numbers 4 and 5) on page 172 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Session 2<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2. Recall the properties of inequalities.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B. Follow-up Lesson<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> </span></b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Explain the proof of Theorem 2-10.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> 2. Illustrative Examples<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Use the examples on page 165 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> 3. Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Solve Written Mathematics of Exercise 2.7 (numbers 6 and 7) on page 172 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (numbers 8 and 9) on page 172 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Session 3<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall the Exterior Angle Equality Theorem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Follow-up Lesson<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Prove Theorem 2-11.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Illustrative Examples<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Practices Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (numbers 11 and 12) on page 172 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (number 13) on page 173 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <b>Session 4<o:p></o:p></b></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall Theorems 2-11 and 2-12.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Follow-up Lesson<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the students to work on Explore on page 167 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Illustrative Example<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Use the examples on page 168 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Practice Exercises<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Answer Mental Mathematics of Exercise 2.7 (number 1-10) on page 171 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (number 14) on page 173 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (numbers 15 and 16) on pages 173-174 of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <b>Session 5<o:p></o:p></b></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Preliminary Activities<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Recall the Area Addition Postulate.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Follow-up Lesson<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Tell the students something about Pythagoras.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Tell the students that one of the proofs of the Pythagorean Theorem was attributed to Bhaskasa, a Hindu mathematician of the twelfth century.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Draw a figure similar to figure 1 on a cardboard. Cut out the four congruent triangles and the square. Make several sets of these cut-outs. Distribute one set to each group.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Divide the class into small groups. Ask each group to form a bigger (figure 1) using all the cutouts. Figure 1 should not be shown to the students.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the groups to label the sides of their triangles as in figure 2.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the following questions:<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a. In terms of <i>a </i>and <i>b, </i>what is the length of the side of the inner square?<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b. In terms of <i>a </i>and <i>b, </i>what is the area of one of the triangles?<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">c. What is the area of the inner square?<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">d. What is the area of the bigger square in terms of <i>c?<o:p></o:p></i></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">e. If you add all the areas of the four congruent triangles and the area of the inner square, will the sum be equal to the area of the bigger square? Why?<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> 7. Ask the students to form an equation.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">8. Ask the students to simplify the left side of the equation to arrive at the Pythagorean Theorem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">9.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the students to remove the inner square.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">10.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the students to write an equation indicating the removal of the inner square. The students should be able to write this equation:<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1.25in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">11.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Tell the students to simplify the equation to arrive at the Pythagorean Theorem.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Checking for Understanding<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1. Find x.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2. Jay-jay left his house and walked 6 km due east and then 8km due month. How far is he from the starting point?<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3. Find the range of the possible lengths of<i>LM.<o:p></o:p></i></span></span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 0.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Assignment<o:p></o:p></span></b></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.7 (number 17-19) on page of the textbook.<o:p></o:p></span></span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><br />
</span></div><div class="MsoNormal" style="font-family: Arial; margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">If there is enough time, solve the Challenge Problems of Exercise 2.7 on </span></b></span><br />
<span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">page 174 of the textbook.</span></b></span><br />
<span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span><br />
<span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><span class="Apple-style-span" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: normal; line-height: 18px;"></span></span></b></span><br />
<div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b><span style="font-size: 12.5pt;">Lesson 2.8<o:p></o:p></span></b></span></b></span></div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b><u><span style="font-size: 13pt;">Angles Formed by Parallel Lines Cut by a Transversal<o:p></o:p></span></u></b></span></b></span></div><div class="MsoNormal"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 10pt;"> (Textbook pages 175-189, 2 sessions)<o:p></o:p></span></span></b></span></div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical Concepts and Skills<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Parallel lines are coplanar lines that do not intersect.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Skew lines are noncoplanar lines.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Through a point outside a line, there is one and only one line parallel to the given line.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A transversal is a line that intersects two or more coplanar lines at two or more distinct points.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Alternate interior angles are two nonadjacent interior angles on opposite side of a transversal.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Alternate exterior angles are two nonadjacent exterior angles on opposite side of a transversal.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Corresponding angles are two nonadjacent angles, one interior and one exterior on the same side of the transversal.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two parallel lines are cut by a transversal, then any pair of alternate interior angles are congruent.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two parallel lines are cut by a transversal, then any pair of alternate exterior angles are congruent.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">J.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two parallel lines are cut by a transversal, then the corresponding angles are congruent.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">K.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two parallel lines are cut by a transversal, then the interior angles on the same side of a transversal are supplementary.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">L.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two parallel lines are cut by a transversal, then the exterior angles on the same side of a transversal are supplementary.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">M.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>In a plane, a line perpendicular to one of the two parallel lines is perpendicular to the other.</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To differentiate parallel lines from skew lines</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To illustrate, identify, and define a transversal</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To identify and define angles formed when two lines are cut by a transversal</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To illustrate the Parallel Postulate and the Parallel-Alternate Interior Angle Postulate</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To prove the following theorems:</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Parallel-Alternate Exterior Angle Theorem</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Parallel-Corresponding Angle Theorem</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Parallel-Interior Angles-Same Side Theorem</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Parallel-Exterior Angle-Same Side Theorem</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Having initiative</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">manila paper marker</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategy<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Discussion</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>Session 1<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the Vertical Angle Theorem.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Proper<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guide the students in identifying and defining parallel lines, skew lines, and transversals.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrate the parallel lines postulate.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Show that when a transversal intersects a pair of lines at two different points, eight angles are formed.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guide the students in defining the following terms:</span></b></span></div><div class="MsoNormal" style="margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Alternate interior angles</span></b></span></div><div class="MsoNormal" style="margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Alternate exterior angles</span></b></span></div><div class="MsoNormal" style="margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Corresponding angles</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrate the Parallel-Alternate Interior Angle Postulate.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Apply the Parallel-Alternate Interior Angle Postulate in proving Theorem 2-14, The Parallel-Alternate Exterior Angles Theorem.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove Theorem 2-15. The Parallel-Corresponding Angles Theorem using Theorem 2-14.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: 9pt;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Ask the students to complete the proof of Theorem 2-16, The Parallel-Interior Angles-Same Side Theorem on page 181 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Prove Theorem 2-17 on page 183 of the textbook.</span></b></span></div><div class="MsoNormal"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>Session 2<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities</b></span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: -9pt;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.Check the assignment.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of linear pair and the definition of supplementary.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to explain Theorem 2-16, The Parallel-Interior Angles-Same Side Theorem.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><span style="height: 139px; left: 0px; margin-left: 372px; margin-top: 28px; position: absolute; width: 216px; z-index: -3;"><img height="139" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1026" width="216" /></span>Ask the students to complete the proof of Theorem 2-18, The Perpendicular-Parallel Lines Theorem on page 183 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: -9pt;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.Illustrative Example</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Prove this problem on the board.</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Given:<i> l<sub>1</sub> </i>ll <i>l<sub>2</sub></i></span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Prove: <1 is supplementary to <3.</span></b></span></div><div class="MsoNormal"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises</span></b></span></div><div class="MsoNormal" style="margin-left: 1.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Answer Mental Mathematics of Exercise 2.8 (numbers 1-4) on page 184 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1.75in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Solve Written Mathematics of Exercise 2.8 (numbers 1-4) of the textbook on page 185.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b> </b>Solve Written Mathematics of Exercise 2.8 (numbers 5-10) pages 185-186 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b> </b>Solve Written Mathematics of Exercise 2.8 (numbers 11-20) on pages 186-188 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>If there is enough time, solve the Challenge Problems of Exercise 2.8 on page 189 of the textbook.<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div align="center" class="MsoNormal" style="margin-left: 1in; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b><span style="font-size: 12.5pt;">Lesson 2.9<o:p></o:p></span></b></span></b></span></div><div align="center" class="MsoNormal" style="margin-left: 1in; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b><u><span style="font-size: 13pt;">Proving Lines Parallel</span></u></b><span style="font-size: 13pt;"><o:p></o:p></span></span></b></span></div><div align="center" class="MsoNormal" style="margin-left: 1in; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><span style="font-size: 10pt;">(Textbook pages 190-196, 2 sessions)</span></span></b></span></div><div align="center" class="MsoNormal" style="margin-left: 1in; text-align: center;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical Concepts and Skills<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two lines are cut by a transversal and a pair of alternate interior angles are congruent, then the lines are parallel.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two lines are cut by a transversal and a pair of alternate exterior angles are congruent, then the lines are parallel.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two lines are cut by a transversal and a pair of corresponding angles are congruent, then the lines are parallel.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two lines are cut by a transversal so that the interior angles on the same side of the transversal are supplementary, then the lines are parallel.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objective<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">To state, prove, and apply the theorems that can be used to prove lines parallel</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">The importance of cooperation</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">manila paper marker</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategy<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Small Group Discussion</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in; text-indent: -0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>Session 1<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activity<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Proper<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Explain Postulate 15, the Alternate Interior-Parallel Postulate.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Prove Theorem 2-19, the Alternate Exterior Angles-Parallel Theorem.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Divide the students into six groups. Ask the first two groups to prove Theorem 2-20, the second two groups to prove Theorem 2-21, and the last two groups to prove Theorem 2-22.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the groups to write their proofs on manila paper. A member of each group will be asked to explain the group’s work.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Apply the theorems in computations.</span></b></span></div><div class="MsoNormal" style="margin-left: 117pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises</span></b></span></div><div class="MsoNormal" style="margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Answer Mental Mathematics of Exercise 2.9 (numbers 1-6) on page 193 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 135pt; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Solve Written Mathematics of Exercise 2.9 (numbers 1-4) on page 194 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b> </b>Solve Written Mathematics of Exercise 2.9 (numbers 5-7) on page 194 of the textbook.</span></b></span></div><div class="MsoNormal"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 0.75in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>Session 2<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activity<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Check the assignment.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><span style="height: 96px; left: 0px; margin-left: 384px; margin-top: 12px; position: absolute; width: 192px; z-index: -2;"><img height="96" src="file:///C:/Users/DEPEDS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" style="-webkit-box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: rgb(238, 238, 238); border-bottom-style: solid; border-bottom-width: 1px; border-left-color: rgb(238, 238, 238); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(238, 238, 238); border-right-style: solid; border-right-width: 1px; border-top-color: rgb(238, 238, 238); border-top-style: solid; border-top-width: 1px; box-shadow: rgba(0, 0, 0, 0.0976563) 1px 1px 5px; padding-bottom: 5px; padding-left: 5px; padding-right: 5px; padding-top: 5px;" v:shapes="_x0000_s1027" width="192" /></span><b>Follow-up Lesson<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrative Example</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Prove this problem.</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Given: <ADC is congruent to <CBA</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> <1 is congruent to <2</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Prove: AD ll CB</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises</span></b></span></div><div class="MsoNormal" style="margin-left: 1.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Solve Written Mathematics of Exercise 2.9 (numbers 12-14) on page 195 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"> Work on Written Mathematics of Exercise 2.9 (numbers 9, 10, and 14) on page 195 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment</b></span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;">Solve Written Mathematics of Exercise 2.9 (numbers 15-17) on page 195 of the textbook.</span></b></span></div><div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div><div class="MsoNormal" style="margin-left: 0.5in; text-indent: 0.5in;"><span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><b>If there is enough time, solve the Challenge Problems of Exercise 2.9 on page 196 of the textbook</b></span></b></span></div><br />
<span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span><br />
<span style="font-size: 10pt; line-height: 14px;"><b><span lang="EN-CA" style="font-family: Calibri, sans-serif; font-size: 10pt;"><br />
</span></b></span></div></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0tag:blogger.com,1999:blog-611756642737780530.post-49585519048174589852011-03-23T18:24:00.000-07:002011-03-23T18:24:41.643-07:00Chapter 1: Geometry of Shape and Size<h3 class="post-title entry-title" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; font: normal normal normal 22px/normal Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 16px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.75em; position: relative;">Chapter 1; Geometry of shape and size</h3><div class="post-header" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 1.6; margin-bottom: 1.5em; margin-left: 0px; margin-right: 0px; margin-top: 0px;"><div class="post-header-line-1"></div></div><div class="post-body entry-content" style="position: relative; width: 490px;"><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><b>CHAPTER 1<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><b>LESSON 1.1 UNDEFINED TERMS<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical concepts and skills<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>The undefined terms in geometry are point, line and plane.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A point has no length, width, or thickness.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A line has length, but no width and no thickness<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A plane has infinite width and length but no thickness.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A good definition has the following characteristics:<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>It should contain ordinary words and geometric terms that have been previously defined or accepted as undefined.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A good definition should list only the essential properties of the term being defined.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A good term is reversible.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><st1:place><st1:city>Segment</st1:city> <st1:state>AB</st1:state></st1:place>, denoted by A̅B̅ or B̅A̅ in the union of points A, B, and all the points between them.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Point P is between A and B if and only if A, P, and B are distinct points of the same line AP + PB = AB<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Collinear points are points on the same line.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A ray starts at one point of a line and goes on infinitely in one direction.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">J.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A postulate is a statement, which is accepted as true without proof.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">K.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A theorem is a statement that needs to be proved.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">L.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Two points exactly one line.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">M.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Two distinct lines intersect in only one point.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">N.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Three points are contained in at least one plane and three non-collinear points are contained in exactly one plane.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">O.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two distinct planes intersect, then their intersection is a line.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">P.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If two points of a line are in a plane, then the line is in the plane.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">Q.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If a line contained in a plane intersects the plane, then the intersection contains only one point.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">R.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Exactly one plane contains a given line and a point not on the line.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">S.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Exactly one plane contains two intersecting lines.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To name and describe the ideas of a point, line, and plane<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To state the characteristics of a good definition<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To define, identify, and name the subsets of a line<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To states the postulates related to points, lines, and planes<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To prove in paragraph from the theorems related to points, line, and planes<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">The importance of cooperation in doing a given task<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Manila paper<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Markers<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Rulers<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Whole class discussion<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Small group discussion<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"><b>Session 1<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the attendance.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discuss briefly the history of geometry.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Paper<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to give examples of symbols and the ideas of symbols and the ideas they represent.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify;">Examples: numeral-number<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify;"> heart-love<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Introduce the three undefined terms of geometry. Write the three terms on a manila paper, and above each term draw the corresponding symbols.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to form small groups. Tell each group to give as many real objects as possible that suggest points, lines, and planes. Tell them the importance of cooperation in doing a given task.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to describe a point, a line, and a plane.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Answer the Mental Mathematics of Exercise 1.1.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrate how to name a point, a line, and a plane.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discuss the three characteristics of a good definition<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guide the students in defining the terms between, segment, collinear points, and ray.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Define the following terms:<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Postulate<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Theorem<o:p></o:p></div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Write on your notebooks the postulates and theorems related to points, lines, and planes. Refer to the textbook pages 6-8<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in; text-align: justify; text-indent: 0.5in;"><b>Session 2<o:p></o:p></b></div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to enumerate the characteristics of a good definition.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students that geometry, just like any other mathematical system, is based not only on undefined terms but also postulates and theorems.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Distinguish a postulate from a theorem.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discuss the postulates related to points, lines, and planes.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discuss the proof of Theorem 1-1, Theorem 1-2, Theorem 1-3, and Theorem 1-4.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to summarize what they have learned on their mathematical journals.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice exercises<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.75in; text-align: justify; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Answer the Mental Mathematics of Exercise 1.1 (numbers 1-10) on pages 10-11 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.75in; text-align: justify; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Solve the Written Mathematics of Exercise 1.1 (numbers 1-10) on page 11 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify;">Solve the Written Mathematics of Exercise 1.1 (numbers 11-12) on page 12 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Solve the Challenge Problems 1 and 2 on page 12 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Bring wires, ruler, and protractor.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><b>Lesson 1.2 ANGLES<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Mathematical concepts and skills<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>An angle is the union of two non-collinear rays with a common endpoint.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A. angle in a plane separates the plane into three sets of points: the points in the interior of the angle, the points in the exterior of the angle, and the points on the angle itself.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To every angle there corresponds a unique real number r where 0<r<180<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>In a half-plane H, through the endpoint of a ray BC lying in the edge of the half-plane, there is exactly one other ray BA, with A in H, such that an angle ABC formed by two rays has a given measure between 0° and 180°.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>If D is in the interior of<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;"><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><span class="apple-style-span"><span style="color: black;">ABC, then m</span></span><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><span class="apple-style-span"><span style="color: black;">ABC = m</span></span><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><span class="apple-style-span"><span style="color: black;">ABD + m</span></span><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><st1:stockticker><span class="apple-style-span"><span style="color: black;">CBD</span></span></st1:stockticker><span class="apple-style-span"><span style="color: black;">.<o:p></o:p></span></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Two angles are congruent if and only if their measures are equal.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Angles can be classified according to their measures.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Acute angle - greater than 0° but less than 90°<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Right angle - equal to 90°<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Obtuse angle - - greater than 90° but less than 180°<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To define, illustrate, and name an angle<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To identify an angle and its parts<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To determine the measure of an angle using a protractor<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To define and identify the different kinds of angles: acute, right, and obtuse<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">The importance of a joint effort in doing a task<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Wires<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Marker<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Protractor<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Ruler<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practical work<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Small group discussion<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Preliminary activities<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the Assignment<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of ray.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"><b>Session 1<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Paper<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Arrange the students into small groups. Have them sit around a table or joined chairs. Make them realize the importance of joint effort in doing a task. Have the wires they bought be cut to 35 cm. tell them to bend the endpoints of each wire to indicate that the wire has no endpoint.<o:p></o:p></div><div style="text-align: justify;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to mark a point between the two arrows using a marker. Ask: “ into how many rays does the point divide the line?”<o:p></o:p></div><div style="text-align: justify;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to form angles by bending their wires.<o:p></o:p></div><div style="text-align: justify;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the following questions<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>How many rays are there in each angle?<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Do the two rays have a common endpoint?<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">c.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Are the two rays collinear<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Draw the following figures on the board:<o:p></o:p></div><div style="text-align: justify;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify;"><br />
</div><div style="text-align: justify;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students which of the following figures are angles. Then ask them to define an angle on their own words.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to draw three angles on their notebooks and ask them to label the angles’ parts<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Illustrative Examples<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify;">Give illustrative examples on how to name angles<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">9.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to use their protractors in measuring the angles they drew on their notebook. Move around the room and check their work.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">10.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Answer the Mental Mathematics of Exercise 1.2 (numbers 1-10) on pages 19-20 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Solve the Written Mathematics of Exercise 1.2 (numbers 1-3) on page 20 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify;">Define the congruent angles, right angles, acute angles, and obtuse angles. Explain why your answers contain the characteristics of a good definition on page 18 of your textbook.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><b> Session 2<o:p></o:p></b></div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of angle.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Have the students copy the two coplanar angles with a common vertex and a common side but no interior points in common as shown below .<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;"><span class="apple-style-span">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Ask the students to measure <span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><span class="apple-style-span"><span style="color: black;">ABD, </span></span><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><st1:stockticker><span class="apple-style-span"><span style="color: black;">CBD</span></span></st1:stockticker><span class="apple-style-span"><span style="color: black;">, and </span></span><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠</span></span><span class="apple-style-span"><span style="color: black;">ABC. Ask them what they notice on the measures of the angles.</span></span><span class="apple-style-span"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;"><span class="apple-style-span">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span class="apple-style-span"><span style="color: black;">Illustrate by means of sticks that if BD is not coplanar with BA and BC, then m</span></span><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">∠ABC≠m∠ABD + m∠</span></span><st1:stockticker><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">CBD</span></span></st1:stockticker><span class="apple-style-span"><span style="color: black; font-family: 'Cambria Math';">. Illu8strate congruent angles by using a protractor.</span></span><span class="apple-style-span"><o:p></o:p></span></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice exercises<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: 0.25in;">Solve the Written Mathematics of Exercise 1.2 (4-8) on page 21 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: 0.25in;">Solve the Written Mathematics of Exercise 1.2 (numbers 10, 12, 14, and 16) on page 22 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: 0.25in;">Solve the Written Mathematics of Exercise 1.2 (numbers 11, 13, 15, and 17-19) on pages 22-23 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">If there is enough time, solve the Challenge problems on page 23 of the textbook<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"><br />
</div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0in; text-align: justify;"><b>LESSON 1.3 POLYGONS<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in; text-align: justify; text-indent: -0.25in;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span><b>Mathematical concepts and skills</b><o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> A polygon is the union of three or pore coplanar segments, which intersect only a endpoints, with each endpoint shared by only two non-collinear segments.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Polygons are classified in the number of their sides.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A polygon is a convex if and only if the lines containing the sides of the polygon do not contain points in its interior.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A polygon is non convex if and only if at least one of its sides is contained in a line, which contains also points of the interior of the polygon.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">The number of diagonals that can be drawn of n sides is given by the formula: Nd= <u>n(n-3)</u>.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;"> 2<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A regular polygon is a polygon that is both equilateral and equiangular.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle is a figure formed by three segments whose joining three non-collinear points.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>An angle bisector of a triangle is a segment contained in a ray that bisects the angle of the triangle, and whose endpoints are the vertex if this angle and a point on the opposite side.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A segment is an altitude of a triangle if and only if it is perpendicular from the vertex to the line that contains the opposite side.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A segment is a median of a triangle if and only if its endpoints are the vertex and the midpoint of the opposite side.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">J.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Triangle can be classified according to the measure of their angles and according to the lengths of their sides.<o:p></o:p></div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Objectives<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To define a polygon<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To define and identify the different kinds of polygon<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To illustrate and identify convex and non convex polygons<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To identify the parts of the regular polygon<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To determine the number of diagonals that can be drawn in a polygon of n side<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To identify, define, and name a triangle<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To define the basic and secondary parts of a triangle (e.g. vertices, sides, medians, angle bisector, and altitude)<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To classify triangles according to the measure of their angles<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To classify triangles according to the lengths of their sides<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">The importance of carefulness<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Wires<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Picture of structural designs<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span> Group work<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discussion<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"><b>Session 1<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary activities<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-align: justify; text-indent: -20.25pt;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the Assignment<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-align: justify; text-indent: -20.25pt;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of a segment.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Paper<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">1. Arrange the students into small groups. Ask them to make three different closed figures using wires with a length of 35 cm. each figure should not contain a curve. In performing the activity, it is most important that they must exercise utmost care.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">2. Tell the students that the figures they formed are called polygons. Explain the root word of polygon.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">3. Present some figures on the board. Ask them which of the figures are polygons and which are not.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">4. Direct the students’ attention to their polygons that are made of wires. Have them count the number of sides of their polygons.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">5. Introduce the terms triangle, quadrilateral, pentagon, etc.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">6. Ask the students to define their own words the different kinds of polygons<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">7. Draw a polygon on the board. Ask the students to draw a point in its interior, and also on the polygon itself.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">8. Move around and inspect the students’ polygons made of wires. Chose one convex and one non convex.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">9. Draw the two chosen polygons on the board. Ask one student to draw the lines containing the sides of the convex polygon.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">10. Ask another student to draw the lines containing the sides of the non convex polygon.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">11. Based on the drawing on the board, ask the students to define a convex and a non convex polygon.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify;">12. Direct the students to read the subtopic on the Parts of a Regular Polygon on pages 28-30. Ask them to define a regular polygon and guide them in identifying and defining its parts.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify; text-indent: 0.5in;">13. Illustrative Examples<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify;">Guide the students in determining the number of diagonals of a polygon. Use the example on page 25 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">14.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practice Exercises<o:p></o:p></div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: 0.5in;">Answer the Mental Mathematics of Exercise 1.3 (numbers 1-4) on page 36 of the textbook.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><b> Session 2<o:p></o:p></b></div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the assignment.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of a triangle.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Follow-up Lesson<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students that polygons are used in structural designs. Show them pictures of structures and then ask them to name all the types of polygons in the pictures.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Draw three triangles on the board, one acute, one right, and one obtuse. Then draw bisectors of their angles using a protractor.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to be careful in bisecting the angles.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guide the students in defining angle bisectors.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Draw another set of triangles. This time ask the students to draw the medians or each triangle.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask how many medians are there in every triangle. Tell the students to define median based on the illustrations on the board.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Draw another set of triangles. This time draw the altitudes of each triangle. Ask the students to identify the altitudes of each triangle. Then ask them to define the altitudes in their own words.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Guide the students in defining a scalene triangle, an isosceles, and an equilateral triangle.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">9.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Tell the students to make a summary of the lesson.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 31.5pt; text-align: justify; text-indent: 22.5pt;"><b>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Checking for Understanding<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: 0.25in;">Identify the geometric figures described by each statement.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle with no congruent side.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle in which all angles are acute.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle with at least two congruent sides.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle in which one of the angles are acute.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle with all sides congruent.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A triangle in which all angles are congruent<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">7.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A segment perpendicular from a vertex of a triangle to the line containing the opposite side.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">8.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A polygon that is both equilateral and equiangular.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">9.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A polygon in which at least one of the sides of a polygon is contained in a line which contains also in the interior of the polygon<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;">10.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>A polygon with ten sides.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Assignment<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: 0.25in;">Solve the Written Mathematics of Exercise 1.3 (numbers 5-8) on page 36 of the textbook.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0in; text-align: justify;"><b>LESSON 1.4 QUADRELATERALS<o:p></o:p></b></div><div class="ListParagraphCxSpLast" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><b> I. Mathematical concepts and skills<o:p></o:p></b></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">A. A quadrilateral is a four sided polygon.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">B. A parallelogram is a quadrilateral with two pairs of parallel sides.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">C. A rectangle is a parallelogram with four right angles.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">D. A square is a rectangle with four congruent sides.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">E. A rhombus is a parallelogram with four congruent sides.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">F. A trapezoid is a quadrilateral with exactly one pair of parallel sides.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">G. The sum of the measures of the angles of a triangle is 180°.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">H. The sum of the measure of the exterior angles of a convex quadrilateral, one at each vertex, is 360°.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">I. The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"> The sum of the measures of the interior angles of a regular polygon with n sides is equal to (n-2)180.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"> The measure of each interior angle of a regular polygon with n sides is <u>(n-2)180</u>.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"> <b> </b>N<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"> The measure of each exterior angle of a regular polygon with n sides is <u>360</u>.<o:p></o:p></div><div class="MsoNormal" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"> n<o:p></o:p></div><div class="ListParagraphCxSpFirst" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b> Objectives<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To illustrate, name, and define a quadrilateral and its parts<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To illustrate, name, and define, the different kinds of quadrilaterals<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To find the sum of the angles of a triangle<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To find the sum of the measures of the interior angles of a convex polygon with n sides.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To find the sum of the measures of the exterior angles of a convex quadrilateral, one at each vertex<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To find the measure of each interior angle of a regular polygon with n sides<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>To find the measure of each exterior angle of a regular polygon of n sides<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>VII.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Values Integration<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">The importance of being diligent<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>VIII.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Materials<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Boxes<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;">Sticks<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>IX.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Practical work in small groups<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;">D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Discussion<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify; text-indent: -0.5in;"><b>X.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Procedure<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-align: justify;"><b>Session 1<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Preliminary activities<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-align: justify; text-indent: -20.25pt;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Check the Assignment<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-align: justify; text-indent: -20.25pt;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Recall the definition of quadrilateral.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in; text-align: justify; text-indent: -0.25in;"><b>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><b>Lesson Paper<o:p></o:p></b></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Play the game “Meeting the Deadline.”<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.75in; text-align: justify; text-indent: -1.75in;"><span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>i.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Divide the students into two groups. Give each group a box containing 20 sticks: four 10 cm, thirteen 6 cm, one 8cm, one 7 cm, and one 12 cm in length.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.75in; text-align: justify; text-indent: -1.75in;"><span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>ii.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Using the 20 sticks, have each group construct quadrilaterals with the following properties:<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Quadrilateral with two pairs of parallel sides<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Quadrilateral with four right angles<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Quadrilateral with four congruent sides<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;">·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Quadrilateral with exactly one pair of parallel sides<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.5in; text-align: justify;">The group that could be able to construct the quadrilaterals ahead of the other groups wins the game.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Have the students copy or draw the quadrilaterals on their notebooks. Tell the students to exercise diligence.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Introduce the terms parallelogram, rectangle, rhombus, and trapezoid<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Using the same sticks, ask the students to construct a rhombus with congruent angles. Tell the students that the resulting figure is a special kind of rhombus called square.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1.25in; text-align: justify; text-indent: -0.25in;">5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>Ask the students to define square in their own words.<o:p></o:p></div><div class="ListParagraphCxSpMiddle" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: justify;"><br />
</div><div class="ListParagraphCxSpLast" style="margin-left: 1in; text-align: justify; text-indent: 0.25in;"><br />
<div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">sections to form a figure that resembles a parallelogram. Refer to the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Illustrative Examples</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Use the examples on page 66 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.7 (numbers 21 and 22) on page 71 of the facebook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. Checking for Understanding</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Find the area of the parallelogram</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">a. base = 10 cm, altitude= 6 cm</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">b. base= 14cm, altitude= 10 cm</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Find the value of x</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Area = 60cm<sup>2<o:p></o:p></sup></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Find the area of the shaded region.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">ABCD is a square</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">AB = 8 cm</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Use pi = 3.14</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">D. Assignment</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.7 (numbers 23 and 14) on page 71 of the textboo.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>If there is enough time, solve the Challenge Problems on page 71 of the textbook.<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span style="font-size: 16pt;">Lesson 18<o:p></o:p></span></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span style="font-size: 16pt;">Surface Areas<o:p></o:p></span></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>I. Mathematical Concepts and Skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. The surface area of a cube is the sum of the areas of its bases and the faces.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">B. The surface area of a rectangular prism is the sum of its lateral area and the area of its bases.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. The surface area of square pyramid is the sum of the lateral area and the areas of the base.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">D. The surface area of a cylinder is SA= 2pi<sup>2 </sup>+ 2piRH</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">E. The total surface area of a cone is equal to pi times the radius squared plus pi times the radius times the slant height</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">F. The surface area of a sphere is four times the area of a circle with the same radius.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>II. Objective<br />
<br />
<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b> </b>To fine the surface area of a cube, rectangular prism, square pyramid, cylinder cone and sphere</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>III. Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Being prudent to avoid errors<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>IV. Material<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Compass<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Models of different prism<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Tape measure<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>V. Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. Discussion<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">B. Practical work<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>VI. Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Session 1<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. Preliminary Activities<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Recall the formula for finding the area of a square, rectangle, and triangle.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">B. Lesson Proper<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Bring models of a cube and a rectangular prism. Divide the class into four groups. Give the first two groups a models of a cube and the other two groups a model of a rectangular prism.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> a. Cube(make one using cardboard)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> b. Rectangular Prism (make a box using cardboar)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. To avoid errors in this activity, tell the students to be prudent. Tell them that the area that covers all the surfaces of a solid is called surface area.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Tell the groups to find the surface area of their models. They may open up their models if they want to.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">4. When “opened up”, the cube looks like this. Tell the group to apply the Area Addition Postulate.<o:p></o:p></div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">5. When “opened up”, the rectangular prism looks like this. Tell the group to apply the Area Addition Postulate<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">6. Illustrative Examples<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Use the examples on pages 72-77 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">7. Practice Exercises<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> a. Answer Mental Mathematics of Exercise 1.8(numbers 1-10) on page 77 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> b. Solve Written Mathematics of Exercise 1.8 (numbers 1 and 2) on page 78 of your textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. Assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve for Written Mathematics of Exercise 1.8 (numbers 3 and 4) on page 78 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 2</b><o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. Preliminary Activities<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Divide the class into two groups. Tell the first group to formulate about areas of triangles. The second group will be asked to solve problems. Then tell the second group to formulate problems related to areas of squares. The first group will be asked to solve the problems.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">B. Follow-up Lesson<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Bring models of a square pyramid made from cardboard<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Tell the students to find the surface areas of their models by opening them up.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. When “opened up”, the square pyramid looks like this. Tell the group to apply the Area Addition Postulate.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">4. Practice Exercises<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8(numbers 5 and 6) on page 78 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. Assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8 (numbers 7 and 8) on page 78 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Session 3<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Recall the area formula of a circle.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Bring models of a cylinder made from cardboard.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Tell the students to find the surface area of their models by opening them up<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. When “opened up”, the cylinder looks like this. Tell the group to apply the Area Addition Postulate. Tell them that they need a compass to determine the center and the radius of each circular base.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> <o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">4. Illustrative Examples<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Use the examples on pages 75-76 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">5. Practice Exercises<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8 (number 9 and 10) on page 79 of the Textbook<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. Assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 18 (numbers 11 and 12 ) on page79 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 4<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. Preliminary Activities<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Review the lesson about areas of circles<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Follow up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Bring models of a cone made of cardboard.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Ask the students to open up their model of a cone.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. When “opened up”, the cone looks like a piece of pie.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> <b>s</b><o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> <b>2 pi r<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">4. The pie-like cardboard can be divided into smaller pie-shaped pieces. Tell the group to cut these pieces and rearranged to look like a parallelogram. Then, ask the group what area of a curved surface is. Tell the students to add this to the area of the Circular base.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b> <o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>5. Practice Exercises<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8 (numbers 13 and 14) on page 79 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8 (numbers 15 and 16) on page 79 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 5<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>A. Preliminary Activities</b>.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the Assignment.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Tell the students who Archimedes was and tell them what he said about the area of a sphere.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Tell the students to use a ball in the next activity.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Tell the group to find the circumference of the (ball) sphere’s greatest circle by using a tape measure.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. The group can then calculate the radius of the ball by using the formula for finding the circumference of a circle.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C= 2 pi r<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Therefore, r = C / 2 pi use= 3.14. The surface area of a sphere = 4 times the area of the greatest side SA= 4(pi r<sup>2 </sup>)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>C. Practice Exercises<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8 (numbers 17 and 18) on page 80 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>D. Checking for Understanding<o:p></o:p></b></div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>E. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> Solve Written Mathematics of Exercise 1.8 (numbers 19 and 20) on page 80 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>If there is enough time, solve the Challenge Problems on page 80 of the textbook.<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span style="font-size: 14pt;">Lesson 19<o:p></o:p></span></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span style="font-size: 14pt;">Volumes<o:p></o:p></span></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>I. Mathematical Concepts and skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. The volume (V) of a rectangular prism is the area of the base (B) times the height(h) (V= Bh, where B = lw)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">B. The volume (V) of triangular prism is the area of the base (B) times the height (h) (V= Bh, where B= area of the triangular base).<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. The volume of any pyramid is equal to 1/3 the area of the base times the height (v = 1/3Bh, where B = area of the base)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">D. The volume (V) of a cylinder is the area of the base (B) times the height (h)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> (V= Bh, where B= pi r <sup>2</sup>)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">E. The volume (V) of a cone equals one-third the area of the base (B) times the height (h) (V= 1/3Bh, where B= pi r <sup>2</sup>)<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">F. The volume of sphere is equal to of 2/ 3 of the volume of a circumscribed cylinder.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>II. Objectives<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> To find the volume of a rectangular prism, a triangular prism, a pyramid, a cylinder, a cone, and a sphere.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>III. Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Realize the importance of having a good reputation<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>IV. Materials<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Manila paper<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Ruler<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>V. Instructional Strategy<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Whole Class Discussion<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>VI. Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Recall the definition of surface area<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Lesson Proper<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Explain the meaning of volume. Tell the students that the volume of a solid is the number of cubic units contained in the solid. Draw this figure on the board.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Ask the following questions:<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">A. How many layers of unit cubes are in the figure?<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">B. How many cubes are in the first layer?<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. How many cubes are in the second layer?<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">D. How many cubes are in two layers?<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">E. What is the volume of the solid figure?<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Change the length of the base to 3cm. Ask the same questions then tell the students to write a formula finding the volume of a rectangular prism.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">4. Show the following illustrations:<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Ask the students how they can find the area of the base of the rectangular Prism<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div style="text-align: center;"><span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span class="Apple-style-span" style="line-height: 18px;"><br />
</span></span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">5. Practice Exercises<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">a. Answer Mental Mathematics of Exercise 1.9 (numbers 1- 14) on pages 87-88 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">b. Solve Written Mathematics of Exercise 1.9 (numbers 1-14) on page 88 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Solve Written Mathematics of Exercise 1.9 (numbers 5-10) on page 89 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 2<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>A. Preliminary Activity<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Recall the formula for finding the area of a circle.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Direct the students top the subtopic Volume of a Cylinder and Volume of a Cone on page 84 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Illustrative Examples<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Use the sample on pages 84-85 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Practice Exercises<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Solve Written Mathematics of Exercise 1.9 (numbers 11 and 12) on page 89 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Solve Written Mathematics of Exercise 1.9(numbers 13-16) on page 89 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 3<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>A. Preliminary Activity<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Check the assignment<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Recall the formula for finding the volume of a cylinder.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">1. Direct the students to the subtopic Volume of a Sphere. Ask what Archimedes said about the relationship between the volume of a sphere and the volume of a circumscribed cylinder.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">2. Illustrative Examples<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Use the example on page 86 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Practice Exercises<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Solve Written Mathematics of Exercise 1.9(numbers 15 and 16) on page 89 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">C. Checking for Understanding<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Solve Written Mathematics of Exercise 1.9(numbers 19 and 20) on page 89 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>D. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">Solve Written mathematics of Exercise 1.9(numbers 19 and 20) on page 89 of the textbook.<o:p></o:p></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>If there is enough time, solve the Challenge Problems on page 90 of the textbook.<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div></div><div class="MsoNormal" style="text-align: justify;"><br />
<div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">6. Guide the students in identifying a quadrilateral and in determining its parts.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">7. Direct the students to work on the Explore on page 38 of the textbook. This time tell them to work in pairs.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">8. Illustrative Examples</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Use the examples on page 41-45 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">9. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>a. Answer Mental Mathematics of Exercise 1.4 (numbers 1-10) on page 45 of the<span> </span>textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>b. Solve Written Mathematics of Exercise 1.4 (numbers 1-4) on page 45 pf the text book.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>C. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>Solve Written Mathematics of Exercise 1.4 (numbers 5-10) on page 46 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>Session 2</b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>A. <span> </span>Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Recall the definition of a regular polygon.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Investigate Corollary 1-7.1</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>a. Draw an equilateral triangle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>b. Find the sum of the measures of its angles using the formula S<sub>a </sub>= (n-2)180.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>c. Find the measure of each angle using a protractor.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>d. What did you notice?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>e. Draw a square.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>f. Find the sum of the measures of its angles using the formula S<sub>a </sub>= (n-2)180.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>g. Find the measure of each angle using a protractor.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>h. What did you notice?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Investigate Corollary 1-7.2</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>a. Draw an equilateral triangle and extend one of its sides.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span></div><div class="MsoNoSpacing"><br />
<div style="text-align: center;"><span class="Apple-style-span" style="border-collapse: collapse; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</span></div></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Using a protractor, find m<CBD.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Divide 360 by 3.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>What do you notice?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>b. Draw a square and extend one of its sides.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span><br />
</span></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Using a protractor, find <DAE.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Divide 360 by 4.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>What do you notice?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">c. Draw a regular pentagon and extend one of its sides.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span><span><br />
</span>Using a protractor, find <CDF. </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Divide 360 by 5.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>What do you notice?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">3. Illustrate how to apply Corollary 1-7.1, Corollary 1-7.2,and Corollary 1-7.3 b explaining the examples on pages 41-45 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">4. Tell the students to write a summary of what they have learned about polygons on their math journals.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;">5. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Solve Written Mathematics of Exercises 1.4 (numbers 11-16) on page 47 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>C. Checking for Understanding<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Solve Written Mathematics of Exercise 1.4 (numbers 17-20) on page 47 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>D. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span></b>Solve Written Mathematics of Exercise 1.4 (numbers 21-24) on page 47 of the textbook.<br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><b><span> </span>If there is enough time, solve the Challenge Problems on page 47 of the textbook.<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>LESSON 1.5<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>MEASUREMENTS<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>(</b>Textbook pages 48-56, 2 sessions)</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.5in;"><b><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Mathematical Concept and Skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span> </span>A circle is the set of all points in a plane with a given distance from a given point in the plane.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A radius of a circle is a segment from the center of the circle to a point on the circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A chord is a segment whose endpoints lie on the circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A diameter is a chord that contains the center of the circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A cylinder is a space figure with tow circular bases that are congruent and parallel.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>F.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A cone is a space figure with one circular base and a vertex.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>G.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A sphere is a set of points in space that are of the same distance from a given point called the center.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>H.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A rectangular prism is a polyhedron with two rectangular bases that are congruent and parallel.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A triangular prism is a polyhedron with two triangular bases that are congruent and parallel.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>J.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A rectangular pyramid is a polyhedron with one rectangular base and four triangular faces</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>K.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A triangular pyramid is a polyhedron with one triangular base and three triangular faces.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>L.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The perimeter of polygon is the distance around it.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>M.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The circumference of a circle is 2πr, where the r = radius.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 38.25pt;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.5in;"><b><span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Objectives<span> </span><o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 58.5pt; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>To define a circle and to be able to identify and define the terms related to it.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 58.5pt; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>To identify the common solids and their parts.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 58.5pt; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>To find the perimeter of a triangle, square, rectangle, and parallelogram.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 58.5pt; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>To find the circumference of a circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 58.5pt;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.5in;"><b><span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><span> </span>The need to be independent</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.5in;"><b><span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Materials<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><span> </span>Manila paper</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><span> </span>Tape measure</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><span> </span>Compass</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><span> </span>Ruler</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.5in;"><b><span>V.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 65.25pt; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Discussion</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 65.25pt; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Individualized Instruction</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.5in;"><b><span>VI.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><b><span> </span>Session 1<span> </span><o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 56.25pt; text-indent: -0.25in;"><b><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall the definition of triangle, square, rectangle, and parallelogram.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 56.25pt; text-indent: -0.25in;"><b><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Lesson Proper<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Show the drawings of the following figures.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Cylinder</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Cone</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Rectangular prism</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Triangular prism</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Rectangular pyramid</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Triangular pyramid</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 94.5pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Sphere</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Ask the students to compare the figures with polygons. Tell them to do this individually. Tell them that it is not always good to be always dependent to other people.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>3.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Label the figures and guide the students in defining them.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>4.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Draw he following figures on manila paper.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Post the Manila paper on the board.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>5.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Guide the students in determining the formula for finding the perimeter of triangle, square, rectangle, and parallelogram.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt; text-indent: -0.25in;"><span>6.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-indent: -0.25in;"><span>a.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Answer Mental Mathematics of Exercise 1.5 (numbers 1-4) on page 54 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-indent: -0.25in;"><span>b.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Solve Written Mathematics of Exercise 1.5 (number 1-6_ on page 55 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 74.25pt;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 56.25pt; text-indent: -0.25in;"><b><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 56.25pt;"><span> </span>Solve Written Mathematics of Exercise 1.5 (numbers 7-10) of the textbook on page 56.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 56.25pt;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Session 2</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 62.25pt; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Preliminary Activities</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 80.25pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 80.25pt; text-indent: -0.25in;"><span>2.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Recall the irrational numbers.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 62.25pt; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>1. In the follow-up activity, divide the students into group of five. Give each group a tape measure, a compass, and a ruler. Then, tell the students to do the following activities:</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 98.25pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Draw several circles.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 98.25pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Measure the circumference of each circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 98.25pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Measure the diameter of each circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 98.25pt; text-indent: -0.25in;"><span style="font-family: Symbol;"><span>·<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></span>Divide the circumference by the length of its diameter.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Tell them briefly about π.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>3. Illustrative Examples</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Use the examples on page 53 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>4. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Solve Written Mathematics of Exercise 1.5 (numbers 11-14) on page<span> </span>56 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>C. Checking for Understanding<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt; text-indent: -0.25in;"><span>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>Find the perimeter of each of the following:</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt;">a. a square 10.5 cm on one side</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt;">b. a rhombus 3.5 cm on one side</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 92.25pt;">c. a parallelogram with sides of 10.5 cm and 8.5 cm</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>2. A rectangular garden is 5 meters long and 26 meters wide. Find the perimeter of the garden.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>3. Find the circumference of a circle with a radius of 12 cm long.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span><span> </span>D. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>Solve Written Mathematics of Exercise 1.5 (numbers 7-10) on page 56 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><b>If there is enough time, solve the Challenge Problems on page 56 of the textbook.<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>LESSON 1.6<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>Areas of Squares and Rectangles<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;">(Textbook pages 57-62, 1 session)</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>I. Mathematical Concept and Skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>A. Every polygonal region has an area, which is a unique positive real number.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>B. The area (A) of a square is the square of the length of its sides.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>C. The area (A) of a rectangle is the product of its base (b) by its height (h).</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>D. If two polygonal regions do not overlap, then the area of their union is equal to the sum of their individual areas.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>II. Objectives<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;">A. To find the area of a square and a rectangle</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;">B. To apply the Area Addition Postulate in computations</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>III. Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Being friendly</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>IV. Materials<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span></b>graphing paper</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>manila paper</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>V. Instructional Strategy<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Discussion</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b>VI. Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Recall the definition of square and rectangle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>3. Provide exercises on factoring quadratic trinomials and quadratic equations.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>B. Lesson Proper<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Illustrate the basic concept of area. Use the following figures.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span><br />
From the illustrations, the students should see that every polygon encloses a surface. And to every surface bounded by a polygon there corresponds a unique positive number called area. </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Explain further the Area Postulate. Use the following illustrations.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>3. Help the students discover the Area Addition Postulate.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><table align="left" border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-bottom-style: none; border-collapse: collapse; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 6.75pt; margin-right: 6.75pt;"><tbody>
<tr style="height: 56.9pt;"><td style="border-bottom-color: black; border-bottom-style: solid; border-bottom-width: 1pt; border-left-color: black; border-left-style: solid; border-left-width: 1pt; border-right-color: black; border-right-style: solid; border-right-width: 1pt; border-top-color: black; border-top-style: solid; border-top-width: 1pt; height: 56.9pt; padding-bottom: 0in; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0in; width: 324.05pt;" valign="top" width="432"><div align="center" class="MsoNoSpacing" style="text-align: center;"><br />
</div><div align="center" class="MsoNoSpacing" style="text-align: center;">2<sup>2<span> </span>+ </sup>2<sup>2 =</sup>2(4)</div></td></tr>
</tbody></table><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>4. Illustrative Examples</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><span> </span>Use the examples on pages 58-59 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><span> </span>5. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><span> </span>a. Answer Mental Mathematics of Exercise 1.6 (numbers 1-4) on page 60 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><span> </span>b. Solve Written Mathematics of Exercise 1.6 (numbers 1-6) on page 61 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>C. Checking for Understanding<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><span> </span>Solve Written Mathematics of Exercise 1.6 (number 7-10) on page 62 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>D. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><b><span> </span></b>Solve Written Mathematics of Exercise 1.6 (numbers (11-12) on page 62 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.5in;"><span> </span><b>If there is enough time, solve the Challenge Problems on page 62 of the textbook.<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>LESSON 1.7<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><b>Areas of Parallelograms, Triangles, Trapezoids, and Circles<o:p></o:p></b></div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;">(Textbook pages 63-71, 4 sessions)</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt; text-indent: -39pt;"><b><span><span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>I.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Mathematical Concept and Skills<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span><span> </span>The area (A) of parallelogram is equal to the product of the length of its base (b) and the length of the corresponding altitude (h).</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The area (A) of a triangle is equal to one-half the product of the length of any base (b) and altitude (h).</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>C.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The area (A) of a trapezoid is equal to one-half the product of the length of its altitude and the sum of the lengths of its bases.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>D.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>The area of a circle = πr<sup>2 </sup>, where r = radius.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>E.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>A circular region is the union of a circle and its interior.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.25in;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt; text-indent: -39pt;"><b><span><span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>II.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Objectives<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>A.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>To discover and apply the formula for the area of a parallelogram,, a right triangle, a triangle, a trapezoid, and a circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 0.75in; text-indent: -0.25in;"><span>B.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span>To differentiate a circle from a circular region.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt; text-indent: -39pt;"><b><span><span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>III.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Values Integration<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt;">Carefulness in doing one’s work</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt; text-indent: -39pt;"><b><span><span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span>IV.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></span></b><b>Materials<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt;">Activity sheets</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 39pt;">Pair of scissors</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>V.<span> </span><span> </span>Instructional Strategies<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 30pt;"><span> </span>A. Practical Work</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 30pt;"><b><span> </span></b>B. Discussion</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>VI. <span> </span>Procedure<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>Session 1<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Check the assignment</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Recall the definitions of altitude, parallelogram, triangle, trapezoid, and</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;">circle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 44.25pt;"><b>B. Lesson Proper<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 62.25pt;">1. Give each student a photocopy of this activity.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 62.25pt;"><span> </span>a. On a separate piece of paper, draw a rectangle similar to the rectangle drawn below.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 62.25pt;"><span></span></div><table align="left" cellpadding="0" cellspacing="0" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><tbody>
<tr><td height="4" width="191"></td></tr>
<tr><td></td><td bgcolor="white" height="78" style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-color: black; border-bottom-style: solid; border-bottom-width: 0.75pt; border-left-color: black; border-left-style: solid; border-left-width: 0.75pt; border-right-color: black; border-right-style: solid; border-right-width: 0.75pt; border-top-color: black; border-top-style: solid; border-top-width: 0.75pt; vertical-align: top;" width="150"><span style="left: 0pt; position: absolute; text-align: center; z-index: 251657216;"><br />
</span> </td></tr>
</tbody></table><o:p style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"> </o:p><br />
<div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 62.25pt; text-align: center;"><br />
</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><div align="center" class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; text-align: center;"><br />
</div><br clear="ALL" /><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>b. Label rectangle ABCD.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>c. Draw a line through point E between A and B.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>d. Cut the drawn rectangle on your paper.<span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>e. Cut along DE.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>f. Move the left piece to the right until point A coincides with point B<span> </span>and point D coincides with point C.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>g. What geometric figure was formed?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>h. What can you say about the area of this figure?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>i. Write a general statement using symbols.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;">2. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>a. Answer Mental Mathematics of Exercise 1.7 (numbers 1-8) on page<span> </span>67 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>b. Solve Written Mathematics of Exercise 1.7 (numbers 1-4) on page 68 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><b>C</b>. <b>Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>Solve Written Mathematics of Exercise 1.7 (numbers 5-8) on page 68 of<span> </span>the text book.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>Session 2<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Recall the Area Formula for a Rectangle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>1. Give each student a photocopy of this activity.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>a. Label your rectangle ABCD. How do you find the area of the rectangle ABCD?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span><span> </span>b. Draw DB.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>c. Cut along DB.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>d. What happened to your rectangle?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>e. What do you call this geometric figure? Why?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>f. Are they congruent? Why?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>g. What can you say about their areas?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>h. How do you find the area of this geometric figure?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>2. Give each student a photocopy of this activity.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span>a. Draw two parallelograms similar to figures 1 and 2 below.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4; margin-left: 1in;"><span> </span></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>b. Label figure 1, ABCD and figure 3, EFGH.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>c. In figure 1, plot any point E between A and B.<span> </span>Draw De and CE.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>d. How many triangles are formed? Name the first triangle, ADE,<span> </span><span> </span>the second, DEC, and the third, EBC.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>e. What kind of triangles are formed? Why?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>f. Cut out rectangle ABCD. Cut along DE and CE.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>g. Show the sum of the areas of ∆ ADE and ∆ EBC is equal to the area of ∆DEC.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>h. Make a conjecture about the area of a triangle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>i. In figure 2, draw diagonal EG. Into how many triangles is the parallelogram divided?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>j. What kind of triangles are formed?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>k. Do you think the areas of the two triangles are equal? Why?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>l. Make a conjecture about the area of the triangle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>3. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Solve Written Mathematics of Exercise 1.7 on page 69 of the text book.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>C. Assignment</b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Solve Written Mathematics of Exercise 1.7 (numbers 15-16) on page 69 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><br />
</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span><span> </span>Session 3<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Review factoring polynomials.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Give each student a copy of this activity.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><span> </span>d. What postulate did you use?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>e. Is the right side of the equation factorable?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>f. What is the common factor?</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>g. Factor the right side of the equation.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Therefore, the Area of a Trapezoid=</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Illustrative Examples</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Refer to the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>3. Practice Exercises</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>Solve Written Mathematics of Exercise 1.7 (numbers 17 and 18) on page 70 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>C. Assignment<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span></b>Solve Written Mathematics of Exercise 1.7 (numbers 17and 18) on page 70 of the textbook.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>Session 4<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span><b>A. Preliminary Activities<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Check the assignment.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>2. Recall the area formula for a rectangle.</div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><b><span> </span>B. Follow-up Lesson<o:p></o:p></b></div><div class="MsoNoSpacing" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 1.4;"><span> </span>1. Guide the students in deriving the formula for the area of a circle by separating a circle into equal sections and then arranging these</div></div></div>STEC-HShttp://www.blogger.com/profile/16315230814981572353noreply@blogger.com0