Math 7
Congruent and Similar Figures Review
Name: _________________________________________
Date: __________________________ Per.: _______
1) In your own words, explain the difference between congruent and similar figures. In your explanation, discuss how you can find if
two figures are similar. Use diagrams to support your explanation.
ΔABC  ΔPQR.
2) Name all pairs of congruent sides.
3) Name all pairs of congruent angles.
4) Find the measure of
 R.
C
3m
B
P
Q
4m
50°
2m
A
R
5) Find the length of PQ .
Draw and label similar figures to answer each question.
6) A triangle has side lengths of 2 cm, 5 cm, and 7 cm. If another triangle’s longest side is 28 cm, what are the lengths of the
triangle’s other two sides?
7) A rectangle has a length of 30 inches and a width of 18 inches. What is the length of a similar rectangle with a width of 3 inches?
8) A rectangular pool has a length of 20 feet and a width of 15 feet. Draw two other rectangular pools, one that is similar to the
original pool and one that isn’t similar. Explain how you can tell that your pools are similar and not similar to the original pool.
9) A 9-foot street sign casts a 12-foot shadow. The lamppost next to it casts a 24-foot shadow. How tall is the lamppost?
10) The manager of an amusement park wants to add a go-kart track that includes a bridge over a lake. Use the picture of the lake and
similar triangles to find the width of the lake.
F
x
90 ft
G
360 ft
J
H
45 ft
K
11) The scale of a room in a blueprint is 3 in:5 ft. A wall in the same blueprint is 18 inches.
a. Complete the table.
Blueprint length (in)
3
Actual length (ft)
b. How long is the actual wall?
c. A window in the room has an actual width of 2.5 feet. What is the width of the window in the blueprint?
12) For a school project, Violet is making a model of the Empire State Building. She is using a scale of 1 cm:8 ft. If the Empire State
Building is 1,252 feet, how tall is Violet’s model?
13) You are taking a road trip from Memphis, Tennessee to New York City. The scale on a road map is 1 cm:500 mi. If the distance
on the map between Memphis and New York City is 2.2 centimeters, how far is the actual distance between the two cities?
Answer Key
1) Answers will vary.
7) 5 in.
12) 156.5 cm.
2) AB and PQ ; BC and QR ; AC and PR
8) Answers will vary.
13) 1100 mi.
3) A  P ; B  Q ; C  R
9) 18 ft.
4) 40°
10) 180 ft.
5) 2 m.
11) a. Inches are 3, 6, 9, 12, 15, 18. Feet are 5, 10, 15, 20, 25, 30.
b. 30 feet
c. 1.5 in.
6) 8 cm. and 20 cm.