Question 1

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

Accepted Answer

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

Answer

The smallest side of a triangle is adjacent with the smallest angle.

Answer

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

Answer

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

Question 2

The sum of the lengths of any two sides of a triangle is always _________.

Accepted Answer

greater than the length of the third side

Answer

less than the length of the third side

Answer

equal to the length of the third side

Answer

half of the length of the third side

Question 3

The measure of an exterior angle of a triangle is always _________.

Accepted Answer

greater than either remote interior angle

Answer

less than either remote interior angle

Answer

equal to its adjacent interior angle

Answer

less than its adjacent interior angle

Question 4

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 ________________.

Accepted Answer

longer than the third side of the second triangle.

Answer

equal to the third side of the second triangle.

Answer

less than the third side of the second triangle.

Answer

greater than or equal to the third side of the second triangle.

Question 5

Which of the following inequalities theorem is applicable in two triangles?

Accepted Answer

SSS Inequality Theorem

Answer

Angle-Side Relationship

Answer

Triangle Inequality Theorem

Answer

Exterior Angle Inequality Theorem

Question 6

Which side of ∆ SET is the longest?

Accepted Answer

$\overline{\mathrm{ST}}$

Answer

$\overline{\mathrm{ST}}$

Answer

Cannot be determined

Answer

$\overline{\mathrm{ST}}$

Question 7

Which side is the shortest?

Accepted Answer

$\overline{\mathrm{ST}}$

Answer

$\overline{\mathrm{ST}}$

Answer

Cannot be determined

Answer

$\overline{\mathrm{ST}}$

Question 8

What theorem is applied?

Accepted Answer

Angle-Side Relationship

Answer

SSS Inequality Theorem

Answer

Triangle Inequality Theorem

Answer

Exterior Angle Inequality Theorem

Question 9

Which of the following angles is an exterior angle of ∆ EAR?

Accepted Answer

∠1

Answer

∠2

Answer

∠4

Answer

∠3

Question 10

Which of the following could NOT be used as the length of the sides of a triangle?

Accepted Answer

8&#44; 14&#44; 10

Answer

11&#44; 12&#44; 13

Answer

6&#44; 5&#44; 12

Answer

4&#44; 4&#44; 4

Question 11

List the sides of ∆TRI in order from longest to shortest measure.

Accepted Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Question 12

In the figure below, which of the following statements is true?

Accepted Answer

∠ETI > ∠KIT

Answer

∠KIT > ∠ITE

Answer

∠IKT > ∠ITE

Answer

∠KIT = ∠ETI

Question 13

Hinges are used to fasten two things together and allow adjustment, rotation, twisting, or pivoting. Which of the following is NOT a hinged device?

Accepted Answer

screw

Answer

compass

Answer

scissor

Answer

folding ladder

Question 14

Jason found out that two sides of two triangles are congruent. As he measures the included angle between these sides, he found out that the measure of the side opposite to the included angle of the first triangle is longer than the measure of the side to the included angle of the second triangle. What theorem did Jason use?

Accepted Answer

Hinge Theorem or SAS Inequality Theorem

Answer

Exterior Angle Inequality Theorem

Answer

Triangle Inequality Theorem

Answer

Converse of Hinge Theorem or SSS Inequality Theorem

Question 15

Each of Angel, Anne, Luis and Sam was given a 15-inch piece of stick. They were instructed to create a triangle. Each cut the stick in their own chosen lengths as follows: Angel—5 in, 5 in, 5 in; Anne—3 in, 5 in, 7 in; Luis—6 in, 4 in, 5in; and Sam—3 in, 4 in, 8 in. Who among them was not able to form a triangle?

Accepted Answer

Sam

Answer

Anne

Answer

Luis

Answer

Angel

Question 16

Which is always true about the measure of an exterior angle of a triangle?

Accepted Answer

It is greater than the measure of either remote interior angle.

Answer

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

Answer

It is less than the measure of either remote interior angle.

Answer

It is greater than the measure of its adjacent interior angle.

Question 17

Which of the following numbers of the same unit could represent the side lengths of a triangle?

Accepted Answer

2&#44; 4&#44; 5

Answer

4&#44;5&#44; 11

Answer

3&#44; 6&#44; 10

Answer

1&#44; 3&#44; 5

Question 18

Which is the largest angle?

Accepted Answer

∠𝑂

Answer

∠𝑃

Answer

Cannot be determined

Answer

∠𝐷

Question 19

Which is the smallest angle?

Accepted Answer

∠𝑃

Answer

∠D

Answer

∠𝑂

Answer

Cannot be determined.

Question 20

What theorem is applicable in determining the smallest and largest angles of ∆𝑃𝑂𝐷?

Accepted Answer

Triangle Inequality Theorem 1 (Ss→Aa)

Answer

Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Answer

Hinge Theorem or SAS Triangle Inequality Theorem

Answer

Triangle Inequality Theorem 2 (Aa→Ss)

Question 21

1. Which side of ∆𝑆𝐴𝑊 is the shortest?

Accepted Answer

$\overline{\mathrm{ST}}$

Answer

$\overline{\mathrm{ST}}$

Answer

Cannot be determined

Answer

$\overline{\mathrm{ST}}$

Question 22

Which side of ∆𝑆𝐴𝑊 is the longest?

Accepted Answer

$\overline{\mathrm{ST}}$

Answer

$\overline{\mathrm{ST}}$

Answer

Cannot be determined

Answer

$\overline{\mathrm{ST}}$

Question 23

What theorem is applicable in determining the shortest and longest sides of ∆𝑆𝐴𝑊?

Accepted Answer

Triangle Inequality Theorem 2 (Aa→Ss)

Answer

Triangle Inequality Theorem 1 (Ss→Aa)

Answer

Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Answer

Hinge Theorem or SAS Triangle Inequality Theorem

Question 24

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?

Accepted Answer

28 meters

Answer

37 meters

Answer

13 meters

Answer

11 meters

Question 25

Given below is ∆𝐴𝑅𝑇. List the sides from the longest to the shortest.

Accepted Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Question 26

What is the measure of ∠𝐴?

Accepted Answer

50°

Answer

105°

Answer

25°

Answer

155°

Question 27

What is the measure of ∠𝐺𝑅𝐷?

Accepted Answer

75°

Answer

105°

Answer

25°

Answer

155°

Question 28

Which is the longest side of ∆𝑅𝐴𝐷?

Accepted Answer

$\overline{\mathrm{ST}}$

Answer

Cannot be determined

Answer

$\overline{\mathrm{ST}}$

Answer

$\overline{\mathrm{ST}}$

Question 29

What theorem supports this statement, “In an obtuse triangle, the longest side is opposite the obtuse angle.”

Accepted Answer

Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)

Answer

Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)

Answer

Hinge Theorem or SAS Triangle Inequality Theorem

Answer

Converse of Hinge Theoremor SSS Triangle Inequality Theorem

Question 30

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?

Accepted Answer

33m

Answer

67m

Answer

35m

Answer

68m

Question 31

What is the largest angle?

Accepted Answer

∠𝐸

Answer

∠𝑁

Answer

∠𝑃

Answer

Cannot be determined

Question 32

What is the smallest angle?

Accepted Answer

∠𝑁

Answer

∠𝐸

Answer

Cannot be determined.

Answer

∠𝑃

Question 33

Which of the following lengths in cm are possible measures of the sides of a triangle?

Accepted Answer

5&#44; 6&#44; 7

Answer

1&#44; 2&#44; 3

Answer

4&#44; 5&#44; 10

Answer

5&#44; 9&#44;15

Question 34

Which of the following theorems will support your answer in number 33?

Accepted Answer

Triangle Inequality Theorem 3 (𝑆1 + 𝑆2> 𝑆3)

Answer

Exterior Angle Inequality Theorem

Answer

Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)

Answer

Converse of HingeTheorem or SSS Triangle Inequality Theorem

Question 35

Which of the following statements is true?

Accepted Answer

𝑚∠𝐾𝑁𝐼 > 𝑚∠𝑃𝐼𝑁

Answer

𝑚∠𝐾𝑁𝐼 < 𝑚∠𝑃𝐼𝑁

Answer

𝑚∠𝐾𝑁𝐼 = 𝑚∠𝑃𝐼𝑁

Answer

Cannot be determined.

Question 36

Which of the following statements is true?

Accepted Answer

𝑚∠𝑁𝑃𝐼 < 𝑚∠𝐼𝑁𝐾

Answer

𝑚∠𝑁𝑃𝐼 > 𝑚∠𝐼𝑁𝐾

Answer

Cannot be determined

Answer

𝑚∠𝑁𝑃𝐼 = 𝑚∠𝐼𝑁𝐾

Question 37

What theorem did you apply to answer item numbers 35 and 36?

Accepted Answer

Exterior Angle Inequality Theorem

Answer

Triangle Inequality Theorem 3 (𝑆1 + 𝑆2 > 𝑆3)

Answer

Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Answer

Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)

Question 38

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

Accepted Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Answer

$\overline{\mathrm{ST}}$ , $\overline{\mathrm{RI}}$ , $\overline{\mathrm{FR}}$

Question 39

What can you conclude in the given figures?

Accepted Answer

$\overline{\mathrm{ST}}$ > $\overline{\mathrm{RI}}$

Answer

$\overline{\mathrm{ST}}$ < $\overline{\mathrm{RI}}$

Answer

$\overline{\mathrm{ST}}$ > $\overline{\mathrm{RI}}$

Answer

$\overline{\mathrm{ST}}$ = $\overline{\mathrm{RI}}$

Question 40

What theorem did you use to answer item number 39?

Accepted Answer

Hinge Theorem or SAS Triangle Inequality Theorem

Answer

Exterior Angle Inequality Theorem

Answer

Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Answer

Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)

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