Similarity Applications

Which triangle is similar to the above triangle ?

• A

• B

• C

• D

∠A corresponds with which angle in triangle DEF?

• ∠D

• ∠E

• ∠F

• None; the triangles are not similar

All angles in similar figures are congruent.  

• True

• False

Which angle corresponds with ∠X?

• ∠N

• ∠W

• ∠E

• ∠Y

A wall stands 4 feet tall and casts a shadow on the ground that is 6 feet long. A tree casts a shadow that is 24 feet long.

Determine the height of the tree.

• 0.0625 ft

• 36 ft

• 16 ft

• 1 ft

Answer explanation

The height of the tree can be calculated using the ratio of the wall's height to its shadow length. Therefore, the tree's height is (4/6) * 24 = 16 ft.

△ABC ∼ △FGH, AB = 24, AC = 16, CB = 10, and FH = 12. Find the length of FG.

• 18

• 20

• 24

• 16

Answer explanation

Since △ABC ∼ △FGH, the corresponding sides are proportional. Using the ratios of the sides, FG = (24/16) * 12 = 18. Therefore, the length of FG is 18.

Triangle S and triangle T are similar.  The base of triangle S measures 0.6 in. with a height of 0.8 in.  If the base of triangle T measures 3.9 in., what is the height?

• 5.2 in.

• 3.7 in

• 1.9 in

• 2.3 in

Answer explanation

Since triangles S and T are similar, their corresponding sides are proportional. Using the ratio of base to height for triangle S, we can find the height of triangle T: 0.6/0.8 = 3.9/x. Solving for x gives x = 5.2 in.

Find the missing side using proportions.

• 45

• 44

• 42

• 32

Find the value of x using proportions.

• 10

• 5

• 4

• 7

• 7

• 112

• 576

• 48