MATH 8 3RD QUARTER

1. Instruction: Choose the letter which corresponds to your answer.
1. Which of the following statements is true about axioms or postulates?
A. These are statements accepted after proved deductively.
B. These are statements assumed to be true and need no further proof.
C. These are concepts that need to be defined.
D. These are concepts that can be defined using the undefined terms.
2. Given that ∆HIJ ≅ ∆LMN, what angle corresponds to ∠J?
a. ∠H C. ∠M
b. ∠I D. ∠N
3. Which refers to an undefined term that has a specific position but has no dimension or direction?
A. point B. line C. plane D. ray
4. If ∆SIN ≅ ∆COS, which of the following is NOT true?
a. ∠I ≅ ∠O C. ̅IN̅̅ ≅ ̅OC̅̅̅̅
b. ∠S ≅ ∠C D. ̅NI̅̅ ≅ ̅SO̅̅̅̅
5. Which of the following illustrates the commutative axiom?
A. (4 + 𝑛) + 3 = 4 + (𝑛 + 3)
B. 𝑥(3 + 𝑦) = 3(𝑥) + 𝑥(𝑦)
C. 𝑝 + (−𝑝) = 0
D. 𝑎 + 7 = 7 + 𝑎
6. If ∆LUV ≅ ∆YAH, then ∆HAY is congruent to ____.
a. ∆AYH C. ∆UVL
b. ∆LVU D. ∆VUL
7. In finding the value of 𝑥 in the equation 4(𝑥 − 1) = 20, Sheila’s first step is as follows:
4(𝑥 − 1)
4
=
20
4
What axiom is applied?
A. Symmetric Axiom
B. Distributive Axiom
C. Existence of a Multiplicative Inverse
D. Existence of a Multiplicative Identity
8. If ∠E ↔ ∠N, ∠V ↔ ∠S and ∠R ↔ ∠M, then ∆EVR ≅ ____.
a. ∆NSM C. ∆NSR
b. ∆MNS D. ∆SRV
9. If ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹, which side is congruent to 𝐴𝐶?
A. 𝐷𝐸 B. 𝐸𝐹 C. 𝐷𝐹 D. 𝐴𝐵
10. Given that ∆VAN ≅ ∆BUS, ∠V = 60o and ∠N = 70o, find ∠U.
a. 50o C. 70o
b. 60o D. 80o

2. 11. How many pairs of congruent parts are there in two congruent triangles?
A. 6 B. 4 C. 3 D. 2
12. If ∆BUN ≅ ∆DLE, BN is 3.15 cm, BU is 5.90 cm find the length of DE.
a. 2.75 cm C. 5.90 cm
b. 3.15 cm D. 9.05 cm
13. In ∆𝐽𝑂𝑌, what is the included angle between 𝐽𝑌 and 𝑂𝑌 ?
A. ∠𝐽𝑂𝑌
B. ∠𝑌𝑂𝐽
C. ∠𝐽𝑌0
D. ∠𝑂𝐽𝑌
14. You are making party hats for your bestfriend’s birthday.
The measurements are shown in Figure 4.
Find the value of x.
a. 3 C. 7
b. 5 D. 9
15. Using the figure below, which triangle congruence postulate justifies that ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵?
A. SAS Congruence Postulate
B. SSS Congruence Postulate
C. SAA Congruence Postulate
D. ASA Congruence Postulate
16. Figure 6 shows that ∆FUN ≅ ∆DUB. Do you agree that ∠FUN = 94o and ∠DBU = 42o?
A. Yes, ∠FUN = 94o and ∠DBU = 42o.
B. No, ∠FUN = 94o and ∠DBU = 44o.
C. No, ∠FUN = 90o and ∠DBU = 42o. D. It is impossible to determine their measures.
17. If ∆𝐹𝐿𝑌 ≅ ∆𝑊𝐼𝑁 and 𝐹𝑌 is 40 cm long, which is the measure of 𝑊𝑁?
A. 40 cm
B. 20 cm
C. 30 cm
D. 50 cm
18. Cielo is tasked to complete the labels for an output in
Math shown in Figure 5. She must see to it that each triangle should have a perimeter of 46
cm. What possible algebraic expressions should she choose to represent the
dimensions of the given figure?
a. HL = (2x+6) cm, LM = (2x+14) cm, KM = (x+7) cm
b. HL = (4x+6) cm, LM = (3x+3) cm, KM = (2x+10) cm
c. HL = (5x+9) cm, LM = (x+14) cm, KM = (7x+1) cm
HL = (3x+9) cm, LM = (8x-3) cm, KM =

3. 19. Given ∆𝐺𝐸𝑂 ≅ ∆𝑇𝑅𝐼, 𝑚∠𝑂 = 41° and 𝑚∠𝐼 = (3𝑥 + 2)°. What is the value of 𝑥?
A. 13 B. 14 C. 22 D. 21
20. Live has two triangular vegetable gardens shown in Figure 2. He wants to fence them to protect his crops.
It takes 7 m of fencing material for one garden. What is the total length of fencing material needed if the two
gardens are of the same size and shape?
a. 7 m C. 21 m
b. 14 m D. 28 m
21. Which statement CANNOT be used to prove the congruence of two triangles?
A. Three angles of one triangle are congruent respectively to three angles of another triangle because it follows
that the three sides of one triangle are congruent respectively to the three sides of the second triangle.
B. Three sides of one triangle are congruent respectively to the three sides of another triangle because it follows
that the three angles of one triangle are congruent respectively to the three sides of the other triangle.
C. Two angles and the included side of one triangle are congruent respectively to the two angles and the included side of another triangle
because it can be shown that the third angle and the other two sides of one triangle are congruent respectively to the third angle and the
other two sides of the other triangle.
D. Two angles and a non-included side of one triangle are congruent respectively to the two angles and the non-included side of another
triangle because it can be shown that the third angle and the other two sides of one triangle are congruent respectively to the third angle
and other two sides of the other triangle.
22. In the figure below, 𝑇𝑂 is a perpendicular bisector of 𝐻𝑆 at T. What triangle congruence postulate or theorem can be used to prove that ∆𝐻𝑂𝑇
≅ ∆𝑆𝑂𝑇?
A. HyL Congruence Theorem
B. LL Congruence Theorem
C. SSS Congruence Postulate
D. ASA Congruence Postulate
23. If in ∆𝑃𝑂𝑆, 𝑚∠𝑃 = 90°, what is its longest side?
A. 𝑃𝑂
B. 𝑃𝑆
C. 𝑆𝑂
D. Cannot be determined
24. In 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝐴𝐵𝐶𝐷, ∆𝐴𝐵𝐶 ≅ 𝐶𝐷𝐴. Which of the following can justify that ∠𝐵𝐴𝐶 ≅ ∠𝐷𝐶𝐴?
A. CPCTC
B. Definition of Angle Bisector
C. Transitive Property
D. Definition of Right Triangle
25. In the figure, if 𝐸 is a midpoint of 𝐴𝐶 and 𝐵𝐷, which pair/s of segments are congruent?
I. 𝐴𝐵 ≅ 𝐶𝐷
II. 𝐴𝐸 ≅ 𝐶𝐸
III. 𝐵𝐸 ≅ 𝐷𝐸
A. I and II
B. II and III
C. I and III
D. III only
26. How many lines are needed to bisect an angle?
A. none
B. one
C. two
D. infinite
27. In the given figure, what is 𝑚∠𝐹𝐷𝐸?
A. 180°
B. 45°
C. 30°
D. 90°

4. 28. In the figure, 𝐻𝐴 is a perpendicular bisector of 𝑀𝑇. Which angles are congruent?
A. ∠𝑀𝐴𝐻 and ∠𝑇𝐴𝐻
B. ∠𝐴𝑇𝐻 and ∠𝐻𝑇𝐴
C. ∠𝐴𝑇𝐻 and ∠𝐴𝑀𝐻
D. ∠𝑀𝐴𝐻 and ∠𝑀𝐴𝐻
29. Refer to ∆𝑍𝑌𝑋. If the 𝑚∠𝑋𝑌𝑍 = 64°, what is 𝑚∠𝑍?
A. 56° B. 57° C. 58° D. 59°
30. Refer to ∆𝐹𝐺𝐻. If 𝐹𝐽 ≅ 𝐻𝐽, what is the measure of 𝐺𝐹?
A. 8 units
B. 10 units
C. 12 units
D. 14 units
J

5. Answer Key
1. B
2. D
3. A
4. C
5. D
6. B
7. C
8. A
9. C
10. A
11. A
12. B
13. C
14. A
15. A
16. C
17. A
18. A
19. A
20. C
21. A
22. B
23. C
24. A
25. B
26. B
27. D
28. A
29. C
30. B