Holt CA Course 1

5-7 Using Similar Figures

Warm UpSolve each proportion.

1. k4

= 7525

2.

3.

Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles.

JN KO

k = 12 x = 76619

= 24x

Holt CA Course 1

5-7 Using Similar Figures

NS1.3 Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

California Standards

4 7

N 21

Holt CA Course 1

5-7 Using Similar Figures

Vocabulary

indirect measurement

Holt CA Course 1

5-7 Using Similar Figures

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

Holt CA Course 1

5-7 Using Similar Figures

Find the unknown length in the similar figures.

Additional Example 1: Finding Unknown Lengths in Similar Figures

ACQS

= ABQR Write a proportion using corresponding sides.

1248

= 14w

Substitute lengths of the sides.

12 · w = 48 · 14 Find the cross product.12w = 672 Multiply.

12w12

= 67212

w = 56QR is 56 centimeters.

Divide each side by 12.

Holt CA Course 1

5-7 Using Similar FiguresCheck It Out! Example 1

ACQS

= ABQR

Write a proportion using corresponding sides.

1224

= 10x

Substitute lengths of the sides.

12 · x = 24 · 10 Find the cross product.

12x = 240 Multiply.

12x12

= 24012

x = 20

QR is 20 centimeters.

Divide each side by 12.

Find the unknown length in the similar figures.

S

A B

C D

10 cm

12 cm

Q R

T

24 cm

x

Holt CA Course 1

5-7 Using Similar Figures

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 product.Multiply.

Divide each side by 8.

Additional Example 2: Measurement Application

Holt CA Course 1

5-7 Using Similar FiguresCheck 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

Let w = the width of the right rectangle.

612

= 3w

6 · w = 12 · 3

6w = 36

6w6

= 366

w = 6

The right rectangle is 6 cm wide.

Write a proportion using correspondingside lengths.

Find the cross product.Multiply.

Divide each side by 6.

?

Holt CA Course 1

5-7 Using Similar FiguresAdditional 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 high.

2515

≈ 50h

Cross multiply.

h ≈ 30 Divide each side by 5.

Holt CA Course 1

5-7 Using Similar FiguresCheck It Out! Example 3

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

Write a proportion.

Use compatible numbers to estimate.

13

≈ h30

Simplify.

1 • 30 ≈ 3 • h

The outside triangle is about 10 feet tall.

14.75 ft

30.25 ft

h ft 515

≈ h30

30 ≈ 3h Multiply.

5 ft

Cross multiply.

10 ≈ h

514.75

= h30.25

Divide each side by 3.