﻿ Congruence and Similarity Worksheet | Problems & Solutions

# Congruence and Similarity Worksheet

Congruence and Similarity Worksheet
• Page 1
1.
A regular hexagon measures 9 cm on each side. A similar hexagon is formed by halving the side length of the original one. What will happen to perimeter of the new hexagon?
 a. perimeter does not change b. perimeter doubles c. perimeter halves d. perimeter triples

Correct answer : (3)
2.
Identify the figures that are similar but not congruent.

 a. Figure 1 and Figure 4 b. Figure 2 and Figure 3 c. Figure 1 and Figure 3 d. Figure 1 and Figure 2

Correct answer : (3)
3.
Which of the following conditions is true for similar triangles?
 a. A pair of triangles have one equal side as well as one equal angle. b. A pair of triangles have only one proportional side. c. A pair of triangles have three equal angles and proportional sides. d. A pair of triangles have two proportional angles.

Correct answer : (3)
4.
Which of the following conditions is always true for congruent triangles?
 a. A pair of triangles have equal sides. b. A pair of triangles have two proportional angles. c. A pair of triangles have an equal angle and two equal sides. d. A pair of triangles have equal hypotenuses as well as an equal angle.

Correct answer : (1)
5.
Find the length of missing side in the similar triangles shown.

 a. 7 m b. 10 m c. 9 m d. 5 m

Correct answer : (1)
6.
Find the length of the missing side in the similar figures shown.

 a. 21 cm b. 27 cm c. 20 cm d. 18 cm

Correct answer : (1)
7.
Which of the statements is true for the figure?

 a. The triangles ABC and PQR are similar. b. enough information is not given c. The triangles ABC and PQR are neither similar nor congruent. d. The triangles ABC and PQR are congruent.

Correct answer : (4)
8.
ΔMNO and ΔSTR are congruent triangles. Find the measure of $\angle$O.

 a. 58° b. 46° c. 56° d. 76°

Correct answer : (2)
9.
The two triangles shown are similar. Find the missing side length.

 a. 60 ft b. 50 ft c. 55 ft d. 72 ft

Correct answer : (1)
10.
The quadrilateral PQRS shown is similar to quadrilateral ABCD. Find the length of AB.

 a. 21 in. b. 25 in. c. 30 in. d. 27 in.