Practice with Similarity
3/31/16, 11:59 AM
Practice with Similarity
Numerical Problems
Topic Index | Geometry Index | Regents Exam Prep Center
Answer the following questions dealing with similar figures.
1. Which of the following triangles are always
similar?
a. right triangles
b. isosceles triangles
c. equilateral triangles
Choose:
a
b
c
Explanation
2.
The sides of a triangle are 5, 6 and 10. Find the length of the Choose:
longest side of a similar triangle whose shortest side is 15.
10
15
18
30
Explanation
3.
Similar triangles are exactly the same shape and size.
Choose:
True
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Practice with Similarity
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False
Explanation
4.
Given: In the diagram,
is parallel to
, BD = 4,
DA = 6 and EC = 8. Find
BC to the nearest tenth.
Choose:
4.3
5.3
8.3
13.3
Explanation
5.
Find BC.
Choose:
4
4.5
13.5
17
Explanation
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Practice with Similarity
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6.
Two ladders are leaned against a Choose:
wall such that they make the
same angle with the ground. The 4.5'
6.4'
10' ladder reaches 8' up the wall.
14.4'
How much further up the wall
22.4'
does the 18' ladder reach?
Explanation
7.
Choose:
8.5'
16'
17.5'
20'
At a certain time of the day, the shadow of a 5' boy is 8' long.
The shadow of a tree at this same time is 28' long. How tall is
the tree?
Explanation
8.
Two triangles are similar. The sides of the first triangle are 7, Choose:
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Practice with Similarity
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9, and 11. The smallest side of the second triangle is 21. Find
the perimeter of the second triangle.
27
33
63
81
Explanation
9.
Two triangular roofs are similar. The
corresponding sides of these roofs are
16 feet and 24 feet. If the altitude of
the smaller roof is 6 feet, find the
corresponding altitude of the larger
roof.
Choose:
6
9
36
81
Explanation
10.
Two polygons are similar. If the ratio of the perimeters is Choose:
7:4, find the ratio of the corresponding sides.
7:4
49 : 16
Explanation
11.
The ratio of the perimeters of two
similar triangles is 3:7.
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Choose:
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Practice with Similarity
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Find the ratio of the areas.
3:7
9 : 49
Explanation
12.
The areas of two similar polygons are in the ratio
25:81. Find the ratio of the corresponding sides.
Choose:
5:9
25 : 81
625 : 6561
Explanation
13.
Given: These two regular
polygons are similar.
What is their ratio of
similitude (larger to
smaller)?
Choose:
8 : 12
2:1
4:8
Explanation
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Practice with Similarity
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14.
Given: These two
rhombi are similar.
Choose:
If their ratio of
similitude is 3 : 1,
find x.
4
6
9
Explanation
15.
In triangle ABC, angle A = 90º and angle B = 35º. In triangle Choose:
DEF, angle E = 35º and angle F = 55º. Are the triangles
YES
similar?
NO
Explanation
16.
Choose:
Given angle A and
angle A' are each 59º,
find AC.
8
10
12
18
Explanation
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Practice with Similarity
17.
3/31/16, 11:59 AM
A vertical flagpole casts a shadow 12
feet long at the same time that a
nearby vertical post 8 feet casts a
shadow 3 feet long. Find the height
of the flagpole in feet.
Choose:
8
12
24
32
Explanation
18.
The side of one cube measures 8
inches. The side of a smaller cube
measures 6 inches. What is the
ratio of the volumes of the two
cubes (larger to smaller)?
Choose:
8:6
16:9
64:27
64:36
Explanation
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Oswego City School District Regents Exam Prep Center
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