# Solving For Missing Sides Of Similar Triangles (Post-test)

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| By Cutkdmaster
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Cutkdmaster
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This quiz is designed to test your ability to use properties of similar triangles to set up proportions in order to solve for missing sides of similar triangles.

• 1.

### These two triangles are similar.  Solve for x.

• A.

X = 96

• B.

X = 91

• C.

X = 2.6666666666666

• D.

X = 84.375

A. X = 96
Explanation
When you set up your proportion, you should get:

x/16 = 90/15

You then solve this proportion to find the value of x.

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• 2.

### These two triangles are similar.  Solve for x.

• A.

X = 26.66666666666666666

• B.

X = 0.6

• C.

X = 19

• D.

X = 15

D. X = 15
Explanation
When you set up your proportion, you should get:

x/3 = 20/4

You then solve the proportion to find the value of x.

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• 3.

### Use the properties of similar triangles to find the height of the tree.

• A.

H = 48 feet

• B.

H = 12 feet

• C.

H = 3/4 feet

• D.

H = 48 inches

B. H = 12 feet
Explanation
When you set up your proportion you should get:

h/3 = 24/6

You then solve the proportion to find the value of h.

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• 4.

### Select all of the properties that are ALWAYS true of similar triangles.

• A.

Their angle measures are congruent.

• B.

They have the same shape.

• C.

Their side lengths are proportional.

• D.

They are the same size.

A. Their angle measures are congruent.
B. They have the same shape.
C. Their side lengths are proportional.
Explanation
The definition of similar triangles is triangles that have the same shape but not necessarily the same size. The fact that the triangles have the same shape means that they must have the same angles. Also, the triangles side lengths must be proportional.

Similar triangles can be the same size, but they are not ALWAYS the same size.

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• 5.
• A.

990 feet

• B.

4647.5 feet

• C.

.03636363636 feet

• D.

2138 feet

A. 990 feet
Explanation
When you set up your proportion, you should get:

x/6 = 2145/13

You then solve for x to find the height of the tower.

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• 6.

### These two triangles are similar.  Solve for x.

• A.

X = 6.666666666666666

• B.

X = 13

• C.

X = 5.4

• D.

X = 15

D. X = 15
Explanation
When you set up your proportion, you should get:

x/9 = 10/6

You then solve the proportion for x.

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• 7.

### These two triangles are similar.  Solve for x.

• A.

X = 5.4

• B.

X = 1.6666666666666666

• C.

X = 7

• D.

X = 15

A. X = 5.4
Explanation
When you set up your proportion, you should get:

x/3 = 9/5