Practice with Similarity
Numerical Problems
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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 

 

 

2.

The sides of a triangle are 5, 6 and 10.  Find the length of the longest side of a similar triangle whose shortest side is 15.

Choose:

10
  15
 18
30

 

 

3.

Similar triangles are exactly the same shape and size.

Choose:

True
False

 

 

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

 

 

5.

 

 Find BC.

Choose:

4 
4.5 
13.5 
17

 

 

6.

Two ladders are leaned against a wall such that they make the same angle with the ground.  The 10' ladder reaches 8' up the wall.  How much further up the wall does the 18' ladder reach?

Choose:

4.5' 
6.4' 
14.4' 
22.4'

 

 

7.

 
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?

Choose:

8.5' 
16' 
17.5' 
20'

 

 

8. Two triangles are similar.  The sides of the first triangle are 7, 9, and 11.  The smallest side of the second triangle is 21.  Find the perimeter of the second triangle.

Choose:

27
33
63
81

 

 

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

 

 

10. Two polygons are similar.  If the ratio of the perimeters is 7:4, find the ratio of the corresponding sides.

Choose:

7 : 4
49 : 16

 

 

11. The ratio of the perimeters of two similar triangles is 3:7. 

Find the ratio of the areas.

Choose:

3 : 7
9 : 49

 

 

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

 

 

13. Given:  These two regular polygons are similar.

What is their ratio of similitude (larger to smaller)?

Choose:

8 : 12
 2 : 1
4 : 8

 

 

14. Given:  These two rhombi are similar.

If their ratio of similitude is 3 : 1,
find x.

Choose:

4
 6
9

 

 

15. In triangle ABC, angle A = 90º and angle B = 35º.  In triangle DEF, angle E = 35º and angle F = 55º.  Are the triangles similar? 

Choose:

YES
NO

 

 

16.


Given angle A and angle A' are each 59º,
find AC.

Choose:

8
10
12
18

 

 

17. 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

 

 

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