12.
In the above figure, are adjacent angles. If , what is in degrees?
a. 12 c. 96
b. 24 d. 100
13. The measure of an angle is 14 less than thrice the measure of its complement. The measure of the angle is .
a. 26 c. 64
b. 52 d. 78
14. If two angles are both congruent and supplementary, then each is .
a. An acute angle c. obtuse angle
b. A right angle d. exterior angle
15. <A and < B are supplementary. If m<A = 2x – 30 and m<B = x + 60, what is m<A?
a.
50 c. 110
b. 70 d. 60
16. In the above figure, intersect at B. What is m<ABE?
a. 130 c. 48
b. 60 d. 44
17. <A and <B are congruent angles. If m<A = 10x – 20 and m<B = 8x +2, then <A is .
a. Acute angle c. obtuse angle
b. Right triangle d. cannot be determined
18. If the measures of <ABE, < EBD, and <DBC are in the ratio. 2:4:6, respectively, what is m<DBC?
a. 15 c. 60
b. 30 d. 90
19. 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?
a. 124 c. 48
b. 56 d. 24
20. What is the measure of the angle if twice the measure of its complement is 35 less than its supplement?
a. 35 c. 70
b. 45 d. 75
21. If two angles form a linear pair and the measure of one of them is 64, what is the measure of the other?
a. 26 c. 116
b. 64 d. 296
22. They are nonadjacent angles formed by two intersecting lines.
a. Supplementary angles c. complementary angles
b. Linear pairs d. vertical angles
23. How large is the angle made by the hands of a clock at 4:15?
a. 30 c. 60
b. 37.5 d. 60.5
24. Which segments of the given lengths cannot be the side of a triangle?
a. 9 cm, 8 cm, 3 cm c. 9 cm, 6 cm, 3 cm
b. 5 cm, 4 cm, 2 cm d. 11 cm, 12 cm, 13 cm
25. In the above triangle, AC = 13 cm and AB = 17 cm. What is the range of values ofsegment BC?
a. 13 cm <BC < 17 cm c. 4 cm <BC < 17 cm
b. 13 cm <BC < 30 cm d. 4 cm <BC < 30 cm
26. The value of x that will make l1 parallel to l2 is .
a. 8 c. 14
b. 11 d. 17
27. What is the possible range of AC in the above figure?
a. 3 < AC <32 c. 3 < AC <31
b. 8 < AC <32 d. 8 < AC <31
28. What is x equal to in the above figure?
a. 70° c. 50°
b. 60° d. 30°
29. In the above figure, ray OA is perpendicular to ray OC and ray OB is perpendicular to OD. If m<BOC = 30, what is the sum of the measures of <AOB and <DOC?
a. 30 c. 60
b. 120 d. cannot be determined
30. In the above figure, ray AB is perpendicular to ray AC. If m<EAD = 2m<DAC and m<BAE = 3m<DAC, what is m< DAC?
a. 15 c. 45
b. 30 d. 90
B. Proving
Write a two-column proof.
a. Given: segment AC parallel to segment ED
<A congruent to <C
Prove: <A is congruent to <EDB
b. Given: ray BD perpendicular to ray BA
ray Be perpendicular to ray BC
Prove: <ABD is congruent to <CBE
IV. Assignment
Answer the problem For Mathitiniks on page 200 of the textbook.
Summative Test 3
Triangle Congruence
(1 session)
I. Target Proficiency
At least 75% of the students be able to get at least 75% correct items in the test.
II. Procedure
A. Check the assignment.
B. Administer the test.
1. Clarify the directions and announce any corrections made in the test paper.
2. Inculcate the importance of honesty. Encourage them to do their best.
III. Questionnaire
A. Multiple Choice
Write the letter of the correct answer on the blank before each number.
_____ 1. Which of the following correspondence is equivalent to CAT↔ DOG?
a. TCA ↔ DGO b. CTA ↔ DGO
c. ATC ↔ ODG d. TAC ↔ OGD
_____ 2. In the figure, ray BD bisects <ABC. If m<CBD =36, what is m<ABC?
a. 72 b. 63
c. 36 d. 18
_____ 3. The bisectors of two supplementary adjacent angles form an angle with the measure of ______.
a. 45 c. 90
b. 60 d. 180
_____ 4. ray DF bisects < CDE. If m<CDF= 2x +10 and m<EDF= 4x – 10, what is m<CDE?
a. 10 c. 30
b. 20 d. 60
_____ 5. What is x in the figure?
a. 40 c. 70
b. 60 d. 80
_____ 6. If the bisector of an angle of a triangle is perpendicular to the opposite side, then the triangle is .
a. Acute c. obtuse
b. Isosceles d. right triangle
_____ 7. In triangle ABC, <B is congruent to <C. If AB=2x + 4 and AC=5x – 8, then AB = _______.
a. Acute c. isosceles
b. obtuse d. right triangle
_____ 8. In triangle CDE, segment CD congruent to ED. If m<C=3x+10 and m<E=5x-30, what is m<D?
a. 80 c. 50
b. 70 d. 40
_____ 9. Triangle EFG is an isosceles triangle with segment EG congruent to segment FG and m<F = 75. What is m<G?
a. 30 c. 50
b. 40 d. 60
_____ 10. In triangle ABC, <C is a right angle. If m<A = 2x+40 and m<B = 4x – 10, what is m<B?
a. 30 c. 50
b. 40 d. 60
_____ 11. Triangle SAR is an isosceles triangle with <A congruent to <R. if SA= 8x – 40 and SR=5x+20, what is SA+SR?
a. 20 c. 120
b. 40 d. 240
_____ 12.
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?
a. 4 c. 8
b. 5 d. 7
_____13.
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?
a. 5 c. 15
b. 10 d. 20
_____ 14.
In the figure, if line ES is the perpendicular bisector of segment BT and BT= 8 and BE=6, what is line ES?
a. 
c. 
c. b. 
d. 
d. _____15. Name the sides of the triangle above in order of increasing length.
a. AB, BC, AC c. AB, AC, BC
b. AC, BC, AB d. BC, AC, AB
B. Proving
Complete the proof of the following.
Given: <1 congruent to <2
Ray AD bisects angle BAC
Prove: ray AD is the perpendicular bisector of segment BC
Proof:
Statements | Reasons |
1.___________________________________________________ | 1.Given |
2.___________________________________________________ ____________________________________________________ | 2. Vertical angles are congruent |
3.<ABD congruent to <ACD | 3. _________________________________________________ |
4.segment AB congruent to segment AC | 4._________________________________________________ |
5.ray AD bisects <BAC | 5.__________________________________________________ |
6.__________________________________________________ | 6. Definition of Angle Bisector |
7.triangle ABD congruent to ACD | 7.__________________________________________________ |
8.segment DB congruent to DC | 8.__________________________________________________ |
9.___________________________________________________ ____________________________________________________ | 9.Definition of Congruent Segments |
10. line AD is the perpendicular bisector of segment BC | 10._________________________________________________ |
Summative Test 4
Quadrilaterals
(1 session)
I. Target Proficiency
At least 75% of the students should be able to get at least 75% correct items in the test.
II. Procedure
A. Check the test.
B. Administer the test.
1. Clarify the directions and announce any corrections made in the test paper.
2. Inculcate the importance of honesty. Encourage them to do their best.
III. Questionnaire
A. Multiple Choice
Write the letter of the correct answer in the blank before each number.
_____1. It is the quadrilateral with exactly one pair of parallel sides.
a. Rectangle c. square
b. Rhombus d. trapezoid
_____2. In the above figure, if AD = 6(x-3)+8 and BC=2(7-x), what is AD+BC?
a. 12 c. 16
b. 14 d. 18
_____3. In the number 2 figure, if DC=4x-10, AB=14,AD=x+2y, and BC=12, what is y?
a. 4 c. 2
b. 3 d. 1
_____4. Quadrilateral ABCD is a parallelogram. Find x and y if AE=x+3y, CE=6, DE= 2x-3y, and BE=3.
a. x=1, y=3 c. x=2, y=3
b. x=3, y=1 d. x=3, y=2
_____5. ABCD is a parallelogram. Its diagonals AC and BC intersect at E. if DE=4x+8 and BE=6x-26, what is BD?
a. 17 c. 76
b. 34 d. 152
_____6. ABCD is a rectangle. If diagonal AC=4x+5 and diagonal BD=6x-1, what is AC+BD?
a. 17 c. 43
b. 34 d. 21
_____7. MATH is a rhombus. If m<H=2(4x+40) and m<A=3(30+2x), what is m<M?
a. 120 c. 5
b. 60 d. 10
_____8. In the above figure, D and B are midpoints of EC and AC respectively. If BD=1, what is BD+AE?
a. 6 c. 36
b. 24 d. 72
_____9. Which of the following statements is false?
a. The diagonals of a rectangle are congruent
b. The diagonals of a square bisect the vertex angle
c. The diagonals of a rhombus are perpendicular
d. The diagonals of a parallelogram are congruent
_____10. 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?
a. 90 c. 92
b. 91 d. 93
_____11. Quadrilateral ABCD is a rectangle. If m<CAB=25, what is m<DBC?
a. 25 c. 65
b. 50 d. 75
_____12. One angle of an isosceles trapezoid has a measure of 50. The measures of the other angles are.
a. 50, 50, 130 c. 50, 130, 130
b. 50, 50, 50 d. 130, 130, 130
_____13. An isosceles trapezoid has sides of lengths 5, 8, 5, and 14. The lenghth of its median is ________.
a. 11 c. 16
b. 22 d. 32
_____14. Which of the following is false?
a. Every square is a rectangle. c. Every square is a parallelogram.
b. Every square is a rhombus d. Every rhombus is a square.
_____15. 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?
a. 14 c. 66
b. 46 d. 92
_____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?
a. 15 c. 110
b. 70 d. 130
_____17. A trapezoid and its median are shown above the figure. Find the value of x.
a. 12 c. 10
b. 11 d. 9
______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?
a. 40 c. 100
b. 60 d. 120
____ 19. What is the area of a kite with diagonals 10 dm and 16 dm?
a. 160
b. 80
c. 52
d. 
26
26____ 20.
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
a. 72
b. 54
c. 36
d. 27
B. Proving
1. Complete the Proof of the following:
Given: Triangle BEC is an isosceles triangle
ABCD is a rectangle
Prove: E is the midpoint of AD
Proof:
Statements
- Triangle BEC is an isosceles triangle
- BE is congruent to CE
- ABCD is a rectangle
- AB is congruent to DC
- Angle A and Angle E are right angles
- Triangle BAE and triangle CDE are right triangles
- Triangle BAE is congruent to triangle CDE
- AE is congruent to DE
- E is the midpoint of AD
Reasons
- ____________________
- ____________________
- ____________________
- ____________________
- ____________________
- ____________________
- ____________________
- ____________________
____________________
2. Write a two-column proof
Given: Angle 1 is congruent to angle 2
AD is congruent to BC
Prove: Quadrilateral ABCD is a parallelogram
IV. Assignment
Answer the problem for Mathitiniks on page 346 of the textbook
Summative Test 5
Similarity
I. Target Proficiency
At least 75% of the students should be able to get 75% correct items in the test.
II. Procedure
- Check the Assignment
- Administer the test.
1. Clarify the directions and announce any corrections made in the test paper
2. Inculcate the importance of honesty. Encourage them to do their best
III. Questionnaire
- Multiple Choice
Write the letter of the correct answer on the blank before each number
_____1. The ratio of the measure of one angle of an equiangular triangle to the sum
of the interior angles of a pentagon is _____.
a. 1: 6 b. 1:9
c. 2: 6 d. 2:9
_____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?
a. 680 b. 750
c. 1 530 d. 1600
_____3. The geometric mean of 16 and 9 is _____.
a. 25 b. 12
c. 8 d. 7
_____4. An angle is 10 more that its complement. The ratio of the angle to its complement is _____.
a. 5:4 b. 4:5 c. 4:9 d.5:9
_____5.
In the above figure, DE ǁ BC. Find x.
a. 3 b. 4
c. 5 d. 6
_____6.
In the above figure, ∠B ≌∠DEA. If AE =6, AB=9, and AD=8. What is DC?
a. 4 b. 3
c. 2 d. 1
_____7.
ΔABC ∼ΔDEF. If a=6, b=4, c=10, and d=8, what is e?
a. 5 1/3 b. 6
c. 6 1/3 d. 7_____8.
In the above figure, AE=15, BC=6, and CD=3. What is CE?
a. 3 b. 5
c. 9 d. 21
_____9.
ΔABC is a right triangle with altitude CD. If AD=5, DB=7, what is AC?
a. 60 b. 35
c.15√2 d. 2√15
_____10.In the above figure, AC ⊥AB and AD ⊥BC. If BC=20, what is DB?
a. 50 b. 40
c. 10 d. 5
_____11. The areas of two similar triangles are equal to36 cm2 and 81 cm2. what is the ratio of a pair of corresponding sides.
a. 6:9 b. 2:3
c. 3:6 d. 8:1
_____12. The corresponding medians of two similar triangles are 3 cm and 7 cm, respectively. The ratio of their areas is ___.
a. 6:14 b. 9:49
c. 9:27 d. 4:10
_____13. The areas of two similar triangles are 81 cm 2 and 121 cm 2, respectively. The ratio of the corresponding altitudes is____.
a.81:121 b. 8:1
c.9:11 d. 1:21
_____14. The ratio of pair of corresponding sides of two similar triangles is 5 : 3. The ratio of their perimeters is____.
a. 25:9 b. 5:3
c. 5:8 d. 8:3
_____15. The ratio of the areas of two similar triangles is 4. The ratio of a pair of
81
a corresponding angle bisectors is____.
a. 4:81 b. 81:4
c. 2:9 d. 4:9_____16.
In the above figure, CD bisects ∠ACB. If AB =16, AC=8 and BC=12, what is AD?
a. 4 b. 6.4
c. 8 d. 9.6
_____17.
In ΔABC above AC=10 cm, BC=10 cm, m∠A=30, and m∠B=30. What is AB?
a. 3√5cm b. 5√3cm
b. 3√10 d. 10√3cm_____18.
ΔABC ∼ΔDEF. The perimeter of ΔDEF is ____.
a. 9 cm b. 14cm
c. 24 cm d. 28 cm_____19.
In the above figure, aǁbǁc. what is x?
a. 5 5/7 b.6
c. 6 5/7 d. 7_____20.
Triangle ABC is a right triangle with altitude CD. If AD=25 cm and BD=36 cm, what is the area of ΔABC?
a. 915 cm 2 b. 900 cm 2
c. 450 cm 2 d. 61 cm 2
B. Proving
Complete the proof of the following:
1. Given: Quadrilateral ABCD is a rectangle.
__ __
AE ǁ FG
Prove: ΔDAE ∼ΔBGF
Proof:
Statements | Reasons |
__ __
|
|
2. Write a two-column proof.
__
Given: Quadrilateral ABCD is parallelogram with diagonal AC.
Prove: ΔABE∼ ΔCDE
IV. Assignment
Answer the problem For Mathitinikins on page 411 of the textbook.
Summative Test 6
Circles
I. Target Proficiency
At least 75% of the students should be able to get at least 75% correct items in the test.
II. Procedure
A. Check the assignment
B. Administer the test
1. Clarify the directions and announce any corrections made in the test paper.
2. Inculcate the importance of honesty. Encourage themto do their best.
III. Questionnaire
A. Multiple Choice
Write the letter of the correct answer in the blank.
_____1. It is a line that intersects the circle in two points.
a. secant b. tangent
c. diameter d. segment
_____2. P is a point in the exterior of a circle. How many tangents to the circle contain P?
a. 1 b. 2c. 3 d. 4
_____3.
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?
a. 4 b.5
c. 6 d. 7
_____4.
If diameter AB of circle O is 24 cm long, and m ∠ABC=30 o, how far chord
__
BC from the center O.
a. 30cm b. 24cm
c. 12cm d. 6cm
_____5,
In the figure, diameters AB and CD intersect at center O of the circle, mA͡C=x, and mC͡B=4x-20. What is m∠AOD in degrees?
a. 40 b.80
c. 120 d. 140
______6.
In circle O above, m∠OAB=40 o , what is the measure of are A͡CB?
a. 260 b. 220
c. 100 d. 80
______7. The central angle of a circle measures 86 o. The measure of the major are arc of the circle is _____.
a. 274O b. 114 O
c. 137 O d.72 O
______8.
In the above figure, ΔABC is circumscribed about circle O. If AD =6cm, CF=8cm, and EB=4cm, what is the perimeter of ΔABC?
a.18 cm b. 36cm
c. 72cm d. 192cm
______9.
Chords AB and CD intersects at E. If AE=10, EB=6, CE=8, and ED=x, what is CD?
a. 15.5 b.8
c. 7. 5 d. 4______10.
In the above figure, B, C, D, and E are points on the circles, what is m∠A?
a. 10 b. 30
c. 50 d. 70______11.
In the above figure, m∠A=____
a. m∠B b. m∠C
c. m∠D d. m∠BEC
B. Proving
Write a two-column proof.
↔
Given: AC is tangent to circle O to B.
__ __
BE ≌BD
↔ __
Prove: tangent AC ǁ chord DE
Construction.
Draw a scalene triangle. Construct the bisectors of its angles.
IV. Assignment
Answer the problem For Mathitinik on page 509 of the textbook.
Summative test 7
Please Coordinate Geometry
I. Target Proficiency
At least 75% of the class should be able to get at least 75% correct items in the test.
II. Procedure
- Check the assignment
- Administer the test:
1. Clarify directions and make the necessary corrections on the questionnaire, if any.
2. Inculcate the importance of honesty
3. Let the students take the test.
III. Questionnaire
Solve the following:
1. Find the slope, the midpoint, and the length of the segment whose endpoints are (6-4) and (2,2).
2. 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?
3. 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.
4. Prove: The two medians of any isosceles triangle are equal.
5. Find an equation of the line through the point (2,3) and parallel to the line x+3y-3=0
6. Find an equation of the line through the point (-1, -4) and perpendicular to the line x-2y+2=0.
7. Find the center and the radius of the circle x2 + y2 + 14x -4y +52=0. Then sketch the circle.
