Republic of the Philippines
DEPARTMENT OF EDUCATION
Region VI – Western Visayas
DIVISION OF NEGROS OCCIDENTAL
Cottage Road, Bacolod City
GRADE 8 - MATHEMATICS
Third Grading Examination
S.Y. 2018 – 2019
Direction: Read and understand the question carefully. Choose the letter of the correct answer from the
given alternatives.
1. Which of the following is a part of mathematical system?
A. Axioms and Postulates
B. Hypothesis C. Conclusion D. Statement
2. It refer to the shorthand reference to a document that refers to other name or idea.
A. Theorems
B. Postulates
C. Defined Terms
D. Undefined Terms
3. A branch of mathematics concerned with questions of shape, size, and relative position of figures and properties
of space.
A. Algebra
B. Statistics
C. Geometry
D. Probability
4. The father of Geometry
A. Euclid
B. Pythagoras
C. Aristotle
D. Rene Descartes
5. Undefined terms represented by double headed arrow.
A. Ray
B. Line
C. Line segment
D. Plane
6. It is one of the undefined terms that indicate position.
A. Point
B. Line
C. Plane
D. Ray
7. A postulate is also known as which of the following?
A. A Conjecture
B. A Proof
C. A Theorem
D. An Axiom
8. It is refer to a statement that is accepted without proof.
A. Postulate
B. Theorem
C. Proof
D. Deductive Reasoning
9. It is a statement accepted after it is proved deductively.
A. Postulate
B. Theorem
C. Proof
D. Deductive Reasoning
10. It states that “Two triangles are congruent if and only if their vertices can be paired so that corresponding sides
are congruent and corresponding angles are congruent”.
A. AAS Congruence
C. SAS Congruence Theorem
B. SSS Congruence
D. Triangle Congruence
11. Listed below are the six pairs of corresponding parts of congruent triangles. Name the congruent triangles.
̅̅̅̅
𝑆𝐴 ≅ ̅̅̅
𝐽𝑂
∠𝐷 ≅ ∠𝑌
A. ∆𝐴𝑆𝐷 ≅ ∆∆𝐽𝑂𝑌
C. ∆𝑆𝐴𝐷 ≅ ∆𝐽𝑂𝑌
̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝑂𝑌
∠𝐴 ≅ ∠𝑂
B. ∆𝐴𝐷𝑆 ≅ ∆𝑌𝐽𝑂
D. ∆𝑆𝐴𝐷 ≅ ∆𝐽𝑌𝑂
̅̅̅̅
̅̅̅
𝑆𝐷 ≅ 𝐽𝑌
∠𝑆 ≅ ∠𝐽
12. Miguel knows that ∆𝑀𝐼𝐺 𝑎𝑛𝑑 ∆𝐽𝐴𝑁, 𝑀𝐼 ≅ 𝐽𝐴, 𝐼𝐺 ≅ 𝐴𝑁, 𝑎𝑛𝑑 𝑀𝐺 ≅ 𝐽𝑁. Which postulate theorem prove the
triangles are congruent?
A. ASA
B. AAS
C. SAS
D. SSS
13. If three sides of one triangle are congruent to the three sides of another triangle, then the triangles are
congruent by:
A. ASA
B. AAS
C. SAS
D. SSS
14. If corresponding congruent parts are marked, how can you prove ∆𝐵𝐸𝐶 ≅ ∆𝐵𝐴𝐶?
A. ASA
C. SAS
B. LL
D. SSS
15. If two sides and an included angle of one triangle are congruent to the corresponding two sides and the included
angle of another triangle, then the triangles are congruent.
A. ASA
B. SAS
C. SSS
D. AAS
16. Use the marked triangles to identify the congruence postulate to illustrate the figure.
A. SAS
C. ASA
B. SSS
D. SAA
17. The congruence postulates states that “If two angles and the included side of one triangle are congruent to the
corresponding two angles and the included side of another triangle, then the triangles are congruent.
A. ASA
B. AAS
C. SAS
D. SSS
18. Given the figure, O is the midpoint of ̅̅̅̅
𝐴𝐷, ̅̅̅̅
𝑂𝐴 bisects ∠𝐵𝑂𝑃, ∠𝐴 ≅ ∠𝐷, prove that ∆𝐴𝐵𝑂 ≅ ∆𝐷𝐶𝑂 by:
A. ASA
B. AAS
C. SAS
D. SSS
̅̅̅̅̅
̅̅̅
̅̅̅̅̅
̅̅̅̅
19. If 𝑀𝐴 ≅ 𝑇𝐼 , ∠𝑀 ≅ ∠𝑇, 𝑀𝑅 ≅ 𝑇𝑁, then ∆𝑀𝐴𝑅 ≅ ∆𝑇𝐼𝑁 by what congruence theorem?
A. ASA
B. AAS
C. SAS
D. SSS
20. The theorem states that “If two angles and a non – included side of one triangle are congruent to the
corresponding two angles and a non – included side of another triangle, then the triangles are congruent”.
A. AAS Congruence Theorem
C. SAS Congruence Theorem
B. SSS Congruence Theorem
D. ASA Congruence Theorem
̅̅̅̅
21. ∠𝑁𝐸𝑅 ≅ ∠𝑁𝑉𝑅, 𝑅𝑁 bisects∠𝐸𝑅𝑉, ∆𝐸𝑁𝑅 ≅ ∆𝑉𝑁𝑅. The two triangles are congruent by _______congruence
theorem.
A. SAS
B. AAS
C. SAA
D. SSS
22. The theorem states that “If a leg and an acute angle of one right triangle are congruent to a leg and an acute
angle of another right triangle, then the triangles are congruent.
A. HyL Congruence Theorem
C. HyA Congruence Theorem
B. LA Congruence Theorem
D. LL Congruence Theorem
23. Give the figure state the congruence theorem that proves that the triangles are congruent.
A
A. LA
B
D
B. LL
C. HyL
D. HyA
C
24. If the legs of one right triangle are congruent to the legs of another right triangle , then the triangles are
congruent by:
A. LA Congruence Theorem
C. LL Congruence Theorem
B. HyL Congruence Theorem
D. HyA Congruence Theorem
25. Consider the right triangles HOT and DAY with right angles at O and A, respectively, such that ̅̅̅̅
𝐻𝑂 ≅ ̅̅̅̅
𝐷𝐴 and
∠𝐻 ≅ ∠𝐷. Prove that ∆𝐻𝑂𝑇 ≅ ∆𝐷𝐴𝑌 by:
A. LA Congruence Theorem
C. LL Congruence Theorem
B. HyL Congruence Theorem
D. HyA Congruence Theorem
26. What congruence theorem states that, “If the hypotenuse and an acute angle of one right triangle are congruent
to the corresponding hypotenuse and an acute angle of another right triangle, then the triangles are congruent.
A. LA Congruence Theorem
C. LL Congruence Theorem
B. Hyl Congruence Theorem
D. HyA Congruence Theorem
27. State the congruence theorem of the figure below.
A. LA Congruence Theorem C. LL Congruence Theorem
B. Hyl Congruence Theorem D. HyA Congruence Theorem
28. If the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and a leg of
another triangle, then the triangles are congruent.
A. LA Congruence Theorem
C. LL Congruence Theorem
B. HyL Congruence Theorem
D. HyA Congruence Theorem
̅̅̅̅ ≅ 𝐷𝐹
̅̅̅̅, and
29. Let ∆𝐴𝐵𝐶 𝑎𝑛𝑑 ∆𝐷𝐸𝐹 be two right angle be two right triangles with 𝑚∠𝐵 = 𝑚∠𝐸 = 90, 𝐴𝐶
̅̅̅̅
̅̅̅̅̅
𝐵𝐶 ≅ 𝐸𝐹. Prove that ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹 by:
A. LA Congruence Theorem
C. LL Congruence Theorem
B. Hyl Congruence Theorem
D. HyA Congruence Theorem
For items 30 – 32
Complete the proof. Choose the letter of the correct answer to fill the blank
A. Reflexive Property
B. ASA
C. SAS
D. ∠𝐵𝐶𝑂 ≅ ∠𝐴𝐶𝑂
In ∆𝐴𝐵𝐶, 𝑙𝑒𝑡 𝑂 be a point in AB such that CO bisects ∠𝐴𝐶𝐵, if 𝐴𝐶 = 𝐵𝐶.
Prove that ∆𝐴𝐶𝑂 ≅ ∆𝐵𝐶𝑂
Statements
Reasons
1. 𝐴𝐶 ≅ 𝐵𝐶
1. Given
2. 𝐶𝑂 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐶𝐵
2. Given
3. ____30____
3. Definition of angle bisector
4. 𝐶𝑂 ≅ 𝐶𝑂
4. ____31_____
5. ∆𝐴𝐶𝑂 ≅ ∆𝐵𝐶𝑂
5. ____32_____
33. In ∆𝐴𝐵𝐶, 𝐴𝐵 = 𝐴𝐶, 𝑖𝑓 𝑚∠𝐵 = 80, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 ∠𝐴.
A. 20
B. 80
C. 100
D. 180
34. What is the measure of each side of an equilateral triangle when its perimeter is 48 cm?
A. 13 cm
B. 14 cm
C. 15 cm
D. 16 cm
35. ∆𝐷𝐸𝐹 is an isosceles triangle, if one of the base angle measures 400, what is the measure of its vertex angle?
A. 70°
B. 80°
C. 40°
D. 100°
36. One of the equal sides of an isosceles triangle whose perimeter is 50 cm and the length of its base is 20 cm.
A. 15
B. 20
C. 25
D. 30
⃗⃗⃗⃗⃗ bisects ∠𝑀𝐴𝑇 at point O. Which of the following angles are congruent?
37. Given that 𝐴𝑂
A. ∠𝑀𝐴𝑂 ≅ ∠𝑇𝐴𝑂
B. ∠𝑀𝐴𝑂 ≅ ∠𝑇𝐴𝑀
C. ∠𝑀𝐴𝑇 ≅ ∠𝑇𝐴𝑂
D. ∠𝑂𝐴𝑇 ≅ ∠𝑀𝐴𝑇
̅̅̅̅
38. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹, which segment is congruent to 𝐴𝐵?
A. BC
B. AC
C. DE
D. EB
̅̅̅̅
̅̅̅̅
39. In ∆𝐴𝐵𝐶, 𝐵𝑋 is perpendicular to 𝐴𝐶 . If 𝑚∠𝐵𝑋𝐶 = 2𝑥 + 5, then what is the value of x?
A. 42.5
B. 55.5
C. 77.5
D. 90
40. Given the measure of the angles of a triangle, name the sides in increasing order:
∠𝑇 = 35°, ∠𝑌 = 115°, ∠𝑅 = 30°
̅̅̅̅, 𝑌𝑅
̅̅̅̅ , ̅̅̅̅̅
̅̅̅̅ , 𝑇𝑅
̅̅̅̅, 𝑇𝑌
̅̅̅̅
̅̅̅̅, 𝑌𝑅
̅̅̅̅ , 𝑇𝑌
̅̅̅̅
̅̅̅̅ , 𝑇𝑌
̅̅̅̅, 𝑌𝑅
̅̅̅̅
A. 𝑇𝑌
𝑇𝑅
B. 𝑌𝑅
C. 𝑇𝑅
D. 𝑇𝑅
-God Bless-