M2 GEOMETRY PACKET 3 FOR UNIT 5
REVIEW PROBLEMS FOR TEST ON UNIT 5, PART 1
(The test will cover 7-1 TO 7-4, 7-6, 7-7, 9-6, 11-5, but this review does not cover 7-4, 7-6, or 9-6.)
In #1-3, use the map and a ruler to find
the actual distance between each pair of
cities. Measure to the nearest sixteenth
of an inch.
1. Port Jacob and Southport
2. Brighton Beach and Pirates’ Cove
3. Eastport and Sand Dollar Reef
4. Sandy is making a 139 centimeters long scale model of the Parthenon for her World History class. The actual
length of the Parthenon is 69.5 meters long.
a. What is the scale of the model?
b. How many times as long as the actual Parthenon is the model?
5. An architect is making a scale model of an office building he wishes to construct. The model is 9 inches tall.
The actual office building he plans to construct will be 75 feet tall.
a. What is the scale of the model?
b. How many times as tall as the actual office building is the model?
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M2 GEOMETRY PACKET 3 FOR UNIT 5
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6. Will is building a scale model of a Boeing 747 aircraft. The wingspan of the model is about 8 feet 10 in. If
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the scale factor of the model is approximately 1:24, what is the actual wingspan of a Boeing 747?
7. A movie director is creating a scale model of the Empire State Building to use in a scene. The Empire State
Building is 1250 feet tall.
a. If the model is 75 inches tall, what is the ratio of the height of the model to the height of the actual
building?
b. How tall would the model be if the director uses a scale factor of 1:75?
In #8-9, each pair of figures is similar. Give ratios as reduced fractions, and label answers with units as
appropriate. Round areas to the nearest tenth if necessary.
8.
9.
a. Ratio of side lengths =
a. Ratio of side lengths =
b. Ratio of areas =
b. Ratio of areas =
c. Proportion involving areas:
c. Proportion involving areas:
d. Area of shaded figure =
d. Area of shaded figure =
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M2 GEOMETRY PACKET 3 FOR UNIT 5
In #10-11 each pair of figures is similar. Give ratios as reduced fractions, and label answers with units.
10.
11.
a. Ratio of areas =
a. Ratio of areas =
b. Ratio of side lengths =
b. Ratio of side lengths =
c. Proportion involving side lengths:
c. Proportion involving side lengths:
d. x =
d. x =
12. Max has two posters for his science project. Each poster is a rectangle. The length of the larger poster is 11
inches. The length of the smaller poster is 6 inches. What is the area of the smaller poster, to the nearest
tenth of a square inch, if the larger poster is 93.5 square inches?
In #13-19, each diagram shows a pair of similar triangles. Determine whether a proportion that solve the
problem should involve whole sides of triangles or parts of sides of triangles, and solve for x.
13.
a. Whole sides or parts of sides?
b. If you answered “whole sides”, redraw and label both triangles
separately.
c. Write a proportion, and solve.
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M2 GEOMETRY PACKET 3 FOR UNIT 5
In #13-19, each diagram shows a pair of similar triangles. Determine whether a proportion that solve the
problem should involve whole sides of triangles or parts of sides of triangles, and solve for x.
14.
a. Whole sides or parts of sides?
b. If you answered “whole sides”, redraw and label both triangles
separately.
c. Write a proportion, and solve.
15.
a. Whole sides or parts of sides?
b. If you answered “whole sides”, redraw and label both triangles
separately.
c. Write a proportion, and solve.
16.
x
a. Whole sides or parts of sides?
b. If you answered “whole sides”, redraw and label both triangles
separately.
c. Write a proportion, and solve.
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M2 GEOMETRY PACKET 3 FOR UNIT 5
In #13-19, each diagram shows a pair of similar triangles. Determine whether a proportion that solve the
problem should involve whole sides of triangles or parts of sides of triangles, and solve for x.
17.
a. Whole sides or parts of sides?
x
b. If you answered “whole sides”, redraw and label both triangles
separately.
c. Write a proportion, and solve.
18.
a. Whole sides or parts of sides?
b. If you answered “whole sides”, redraw and label both triangles
separately.
x
c. Write a proportion, and solve.
19.
a. Whole sides or parts of sides?
b. If you answered “whole sides”, redraw and label both triangles
separately.
c. Write a proportion, and solve.
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M2 GEOMETRY PACKET 3 FOR UNIT 5
In #20-27, state whether the pair of triangles in the figure are similar. If so, complete the similarity
statement and similarity postulate.
20.
22.
24.
26.
Yes or No
21.
Yes or No
If yes,
fill in the blanks:
If yes,
fill in the blanks:
UTS   ______
CBA   ______
by ______ Similarity
by ______ Similarity
Yes or No
23.
Yes or No
If yes,
fill in the blanks:
If yes,
fill in the blanks:
VUT   ______
 JKL   ______
by ______ Similarity
by ______ Similarity
Yes or No
25.
Yes or No
If yes,
fill in the blanks:
If yes,
fill in the blanks:
 KLM   ______
TUV   ______
by ______ Similarity
by ______ Similarity
Yes or No
27.
Yes or No
If yes,
fill in the blanks:
If yes,
fill in the blanks:
 ABC   ______
STU   ______
by ______ Similarity
by ______ Similarity
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