4-9 Using Similar Figures

Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

Similar figures have the same shape but not necessarily the same size.•Corresponding angles are the same•Corresponding sides are proportional

Corresponding means in the same relative position on the figure

4-9 Using Similar Figures

Find the unknown measures in the similar figures.

Additional Example 1: Finding Unknown Lengths in Similar Figures

ABJG

= BCHG Write a proportion using corresponding sides.

105 = 6

x Substitute lengths of the sides.

10 · x = 5 · 6 Find the cross product.10x = 30 Multiply.

10x10

= 3010

x = 3HG is 3 centimeters.

Divide each side by 12 to isolate the variable.

HB A

C GJ

10 cm

6 cm 116 cm58 cm x

5 cm

31°

59°

y

4-9 Using Similar Figures

Find the unknown measures in the similar figures.

Additional Example 1 Continued

Step 2 Find y.Corresponding angles of similar triangles have equal angle measures.

H corresponds to C

y = 59

HB A

C GJ

10 cm

6 cm 116 cm58 cm x

5 cm

31°

59°

y

4-9 Using Similar Figures

City officials want to know the height of a traffic light. Find the height of the traffic light (round to the nearest hundredths).

27.2515 = 48.75

hWrite a proportion.

27.25h = 731.25

The traffic light is about 27 feet tall.

27.25 ft48.75 ft

h ft Cross multiply.

h ≈ 26.83

Divide each side by 27.25 to isolate the variable.

227.25 227.25

4-9 Using Similar FiguresCheck It Out: Example 1

Triangles DEF and GHI are similar.

Triangles DEF and GHI are similar. Find the length of side HI.

2 inE

D F

7 in

H

G I

8 in x

4-9 Using Similar Figures

A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree?

Additional Example 2: Problem Solving Application

11 Understand the ProblemThe answer is the height of the tree.List the important information:• The length of the building’s shadow is 75 ft.• The height of the building is 30 ft.• The length of the tree’s shadow is 35 ft.

4-9 Using Similar FiguresAdditional Example 2 Continued

Use the information to draw a diagram.22 Make a Plan

h

75 feet

30 feet

35 feet

4-9 Using Similar Figures

30 75 = h

35

Solve33

Corresponding sides of similar figures are proportional.

75h = 1050 Find the cross products.

The height of the tree is 14 feet.h = 14

75h75 = 1050

75 Divide both sides by 75.

Additional Example 2 Continued