FREE NJGPA Applying Geometric Theorems Questions and Answers

Question 1

A 15-foot ladder is leaning against a wall. The base of the ladder is 9 feet away from the base of the wall. How high up the wall does the ladder reach?

Accepted Answer

12 feet

Answer

10 feet

Answer

18 feet

Answer

24 feet

Question 2

A triangle has side lengths of 8 cm, 15 cm, and 17 cm. Which statement is true about this triangle?

Accepted Answer

It is a right triangle.

Answer

It is an acute triangle.

Answer

It is an obtuse triangle.

Answer

It is not a valid triangle.

Question 3

In two triangles, two pairs of corresponding angles and the pair of corresponding non-included sides are congruent. Which theorem proves the triangles are congruent?

Accepted Answer

Angle-Angle-Side (AAS)

Answer

Side-Angle-Side (SAS)

Answer

Angle-Side-Angle (ASA)

Answer

Side-Side-Side (SSS)

Question 4

Given that ΔABC ≅ ΔXYZ, AB = 2x + 1, and XY = 15. What is the value of x?

Accepted Answer

x = 7

Answer

x = 6

Answer

x = 8

Answer

x = 14

Question 5

A 6-foot tall person casts a 4-foot shadow. At the same time, a nearby flagpole casts a 20-foot shadow. How tall is the flagpole?

Accepted Answer

30 feet

Answer

24 feet

Answer

28 feet

Answer

40 feet

Question 6

Two triangles are similar. The sides of the first triangle are 5, 12, and 13. The shortest side of the second triangle is 15. What is the perimeter of the second triangle?

Accepted Answer

90

Answer

30

Answer

60

Answer

120

Question 7

In ΔPQR, ∠Q is a right angle. Point S is on PR such that QS is perpendicular to PR. Which statement proves that ΔPQS ~ ΔQRS?

Accepted Answer

Angle-Angle (AA) Similarity

Answer

Side-Angle-Side (SAS) Similarity

Answer

Side-Side-Side (SSS) Similarity

Answer

They are not necessarily similar.