5-6

5-6 Using Similar Figures

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

5-6 Using Similar Figures

Warm UpSolve each proportion.

1. k4

= 7525

2. 619

= 24x

3.

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

J

N Z K O

A

JN KO

k = 12 x = 76

Problem of the Day

Harvey starts to fill a 3-gallon tank from a hose that delivers 1 gallon per minute. However, the tanks leaks 1 quart per minute. In how many minutes will the tank begin to overflow?4

Course 2

5-6 Using Similar Figures

Learn to use similar figures to find unknown lengths.

Course 2

5-6 Using Similar Figures

Vocabulary

indirect measurement

Insert Lesson Title Here

Course 2

5-6 Using Similar Figures

Course 2

5-6 Using Similar Figures

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

Find the unknown length in 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 = 56

QR is 56 centimeters.

Divide each side by 12 to isolate the variable.

Course 2

5-6 Using Similar Figures

Check It Out: Example 1

Insert Lesson Title Here

Course 2

5-6 Using Similar Figures

A B

C D

10 cm

12 cm

Q R

S T

24 cm

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 to isolate the variable.

Find the unknown length in similar figures.x

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

Insert Lesson Title Here

Course 2

5-6 Using Similar Figures

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.

Insert Lesson Title Here

Course 2

5-6 Using Similar Figures

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 products.Multiply.

Divide each side by 6 to isolate the variable.

?

Additional Example 3: Estimating with Indirect Measurement

Course 2

5-6 Using Similar Figures

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

Course 2

5-6 Using Similar Figures

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

514.75

= h30.25

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 Divide each side by 3 to isolate the variable.

5 ft

Cross multiply.

10 ≈ h

Lesson Quiz: Part I

Find the unknown length in each pair of similar figures.

Insert Lesson Title Here

Course 2

5-6 Using Similar Figures

1.

2.

x = 120 cm

t = 150 cm

Lesson Quiz: Part II

Find the unknown length in each pair of similar figures.

Insert Lesson Title Here

Course 2

5-6 Using Similar Figures

3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake.

about 15 inches