TABLE OF SPECIFICATION (TOS)

MATHEMATICS 8

No.
Competency % of Remembering Understanding Applying Analyzing Evaluating Creating
Items
1. Illustrates
theorems on
triangle inequalities
( Exterior Angle
Inequality 50% 15 1,2,3,4, 25 5,6,7,8 9 10, 11, 23 22, 24
Theorem, Triangle
Inequality
Theorem, Hinge
Theorem)
2.Applies theorems 26, 27, 28, 29,
on triangle 50% 15 12,13,15 14,16,17 18,19 20,21
inequalities 30
100
Total 30 10 4 4 6 4 2
%

Prepared by: Checked by:

Suzy Jean D. Malaque Valentin S. Catuburan

SST-I Math 8 School Head
1. Which theorem states that if one side of a triangle is longer than the second side, then the angle opposite
the first side is larger than the angle opposite the second side?

A. Triangle Inequality Theorem

B. Angle-Side Relationship Theorem
C. Exterior Angle Inequality Theorem
D. Hinge Theorem or SAS Inequality Theorem

2. Which of the following theorems on triangle inequalities states that the measure of an exterior angle of a
triangle is greater than the measure of either remote interior angle?

A. Triangle Inequality Theorem

B. Angle-Side Relationship Theorem
C. Exterior Angle Inequality Theorem
D. Hinge Theorem or SAS Inequality Theorem

3. If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first
triangle is longer than the third side of the second, then the included angle of the first triangle is larger than
the included angle of the second. Which of the following theorems pertains to two triangles whose two
corresponding sides are congruent and whose third sides are unequal?

A. Triangle Inequality Theorem

B. Exterior Angle Inequality Theorem
C. Hinge Theorem or SAS Inequality Theorem
D. Converse of Hinge Theorem or SSS Inequality Theorem

4. Which of the following theorems states that if two sides of one triangle are congruent to two sides
of another triangle, but the included angle of the first triangle is greater than the included angle of
the second, then the third side of the first triangle is longer than the third side of the second?

A. Triangle Inequality Theorem

B. Exterior Angle Inequality Theorem
C. Hinge Theorem or SAS Inequality Theorem
D. Converse of Hinge Theorem or SSS Inequality Theorem

5. Which of the following statements is true based on Angle-Side Relationship Theorem?

A. The largest side of a triangle is opposite with the smallest angle.

B. The largest side of a triangle is adjacent with the smallest angle.
C. The smallest side of a triangle is opposite with the smallest angle.
D. The smallest side of a triangle is adjacent with the smallest angle.

6. Which of the following theorems deals with the two triangles whose two corresponding sides are congruent
and whose included angle are unequal?

A. SAS Inequality Theorem

B. SSS Inequality Theorem
C. Angle-Side Relationship Theorem
D. Exterior Nagle Inequality Theorem

7. Which of the following could NOT be used as the length of the sides of a triangle?
A. 3, 3, 3
B. 4, 5, 10
C. 5, 7, 9
D. 10, 20, 20
8. Which is always true about the measure of an exterior angle of a triangle?

A. It is less than the measure of its adjacent interior angle.

B. It is less than the measure of either remote interior angle.
C. It is greater than the measure of its adjacent interior angle.
D. It is greater than the measure of either remote interior angle.

9. Refer to the figure at the right, what theorem of triangle inequalities is applied in determining the longest
and shortest side of triangle ΔTWO?
A. SSS Inequality Theorem
B. Triangle Inequality Theorem
C. Angle-Side Relationship Theorem
D. Exterior Angle Inequality Theorem

10. In Δ FRY, which of the following shows the correct arrangement of its sides in descending order?

A. 𝐹𝑌̅̅, 𝐹𝑅̅̅, 𝑅𝑌̅̅

B. 𝐹𝑅̅̅, 𝑅𝑌̅̅, 𝐹𝑌̅̅
C. 𝐹𝑌̅̅, 𝑅𝑌̅̅, 𝐹𝑅̅̅
D. 𝑅𝑌̅̅,̅ 𝐹𝑅̅̅,̅ 𝐹𝑌
11. In the Triangle Inequality Theorem, which of the following describes the relationship of the sum of its two
sides to its third length? Seventeen
A. greater than
B. greater than or equal to
C. less than
D. less than or equal to

12. You are asked to fence a triangular lot. Two sides of the lot have lengths 20 meters and 14 meters. What
is the maximum whole number of meters of fence do you possibly need?

A. 34 meters
B. 35 meters
C. 67 meters
D. 68 meters

13. Which of the following could be a possible measure of the third side of the triangle if the two sides
measure 12 meters and 25 meters?

A. 11 meters
B. 13 meters
C. 28 meters
D. 37 meters

For items 14 – 15, consider the given ΔPET and ΔDOG below.

14. What can you conclude in the given figures?

A. |𝑃𝑇|=|𝐷𝐺|
 B. |𝑃𝑇|>|𝐷𝐺|
C. |𝐷𝐺|<|𝑃𝑇|
D. |𝐷𝐺|>|𝑃𝑇|

15. What theorem did you use to answer item number 13?

A. Exterior Angle Inequality Theorem

B. Triangle Inequality Theorem 1 (𝑆𝑠→𝐴𝑎)
C. Hinge Theorem or SAS Triangle Inequality Theorem
D. Converse of Hinge Theorem or SSS Triangle Inequality Theorem

16. Which of the following statements is true?

A. 𝑚∠𝐾𝑁𝐼 = 𝑚∠𝑃𝐼𝑁.
B. 𝑚∠𝐾𝑁𝐼 > 𝑚∠𝑃𝐼𝑁.
C. 𝑚∠𝐾𝑁𝐼 < 𝑚∠𝑃𝐼𝑁.
D. Cannot be determined.
17. Given the diagram at the right, which statement is true?
A. WX < WY
B. XZ < XY
C. WY > YZ
D. XY > WY

18. Ruel, Geralyn, Reymond and Shiela were given a 24-inch piece of stick each. They were
instructed to create a triangle. Each cut the stick in their own chosen lengths as follows: Ruel—8
in, 8 in, 8 in; Geralyn—5 in, 7 in, 12 in; Reymond—9 in, 7 in, 8 in; and Shiela—6 in, 8 in, 10 in. Who
among them could NOT be able to form a triangle?
A. Ruel
B. Geralyn
C. Shiela
D. Reymond

19. Carlos concluded that the longest side in 𝛥𝑀𝐴𝑃 is 𝐴𝑃̅̅̅ after finding that the angle opposite to 𝐴𝑃̅̅̅ is the
largest angle. What theorem justifies Carlos’ conclusion?

A. Triangle Inequality Theorem 1 (𝑆𝑠→𝐴𝑎)

B. Triangle Inequality Theorem 2 (𝐴𝑎→𝑆𝑠)
C. Hinge Theorem or SAS Triangle Inequality Theorem
D. Converse of Hinge Theorem or SSS Triangle Inequality Theorem

20. The measures of the angles of Δ𝐷𝐸𝐹 are as follows: 𝑚∠𝐷=2𝑥+3°; 𝑚∠𝐸=2𝑥+5°; and 𝑚∠𝐹=𝑥 –8°.
Arrange the sides in increasing order of length.

A. 𝐷𝐸̅̅, 𝐸𝐹̅̅, 𝐷𝐹̅̅

B. 𝐸𝐹̅̅, 𝐷𝐸̅̅, 𝐷𝐹̅̅
C. 𝐷𝐸̅̅, 𝐷𝐹̅̅, 𝐸𝐹̅̅
D. 𝐷𝐹̅̅, 𝐷𝐸̅̅, 𝐸𝐹̅̅

21. Two sides of a triangle have lengths 7 and 15. Write the inequality that represents the possible
lengths for the third side, x?
A. 7< x <15
B. 8< x <15
C. 8< x <15
D. 8< x <22
22. In Δ 𝑁𝐸𝑇, 𝑁𝐸̅̅̅ = 14 cm, 𝐸𝑇̅̅̅ = 15 cm, 𝑁𝑇̅̅̅ = 16 cm. What is the correct order of the angles when arranged from
least to greatest?
A. ∠E, ∠N, ∠T C. ∠T, ∠E, ∠N
B. ∠E, ∠T, ∠N D. ∠T, ∠N, ∠E
23. Which of the following statements is FALSE?
A. Any length of the sides can be used to form a triangle.
B. The largest angle of a triangle is opposite to the longest side.
C. The smallest side of a triangle is opposite to the smallest angle.
D. The sum of any two sides of a triangle is greater than the third side

24. What is the possible value of the third side of a triangle if the other two sides have lengths 5 and 7?
A. x=13 C. x >12
B. x ≥ 13 D. x ≥ 12

25. Which of the following is NOT a theorem on triangle inequalities?

A. Triangle Inequality Theorem
B. Converse Triangle Inequality Theorem
C. Hinge Theorem
D. Exterior Angle Theorem

26.Which theorem states that the sum of the lengths of any two sides of a triangle must be greater than the
length of the third side?
A. Triangle Inequality Theorem
B. Converse Triangle Inequality Theorem
C. Hinge Theorem
D. Exterior Angle Theorem

27Which theorem states that if two sides of a triangle are unequal, then the larger angle is opposite the longer
side?
A. Triangle Inequality Theorem
B. Converse Triangle Inequality Theorem
C. Hinge Theorem
D. Exterior Angle Theorem

28.Which theorem states that if two sides of one triangle are congruent to two sides of another triangle, and
the included angle of the first triangle is greater 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?
A. Triangle Inequality Theorem
B. Converse Triangle Inequality Theorem
C. Hinge Theorem
D. Exterior Angle Theorem

29.Which theorem states that the measure of an exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles?
A. Triangle Inequality Theorem
B. Converse Triangle Inequality Theorem
C. Hinge Theorem
D. Exterior Angle Theorem

30.Which theorem states that if the sum of the lengths of two sides of a triangle is equal to the length of the
third side, then the triangle is degenerate?
A. Triangle Inequality Theorem
B. Converse Triangle Inequality Theorem
C. Hinge Theorem
D. Exterior Angle Theorem