Using Similar Figures

4-5

*Notes 19

Vocabulary

Indirect measurement- a method of using proportions to find an unknown length or distance in 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

= 6x

Substitute lengths of the sides.

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

10x10

= 3010

x = 3

HG is 3 centimeters.

Divide each side by 12 to isolate the variable.

HB A

CGJ

10 cm

6 cm 116 cm

5.8 cmx

5 cm

31°

59°

y

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

CGJ

10 cm

6 cm 116 cm

5.8 cmx

5 cm

31°

59°

y

Find the unknown measures in the similar figures.

Check It Out: Example 1

DB A

CEF

14 cm

9 cm 116 cm

5.8 cmx

7 cm

27°

63°

y

The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.

Let x = the base of the inside triangle.

82

=12x

8 · x = 2 · 128x = 24

8x8

= 248

x = 3The base of the inside triangle is 3 inches.

Write a proportion using corresponding sidelengths.

Find the cross products.Multiply.

Divide each side by 8 to isolate the variable.

Additional Example 2: Measurement Application

Check It Out: Example 2

The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.

3 cm

6 cm12 cm

?

Additional Example 3: Estimating with Indirect Measurement

City officials want to know the height of a traffic light. Estimate the height of the traffic light.

27.2515

= 48.75h

Write a proportion.

Use compatible numbers to estimate.

53

≈ 50h

Simplify.

5h ≈ 150

The traffic light is about 30 feet tall.

27.25 ft

48.75 ft

h ft 2515

≈50h

Cross multiply.

h ≈ 30 Divide each side by 5 to isolate the variable.

Check It Out: Example 3

The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle.

14.75 ft

30.25 ft

h ft5 ft