5-6

5-6 Using Similar Figures

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2


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


Learn to use similar figures to find unknown lengths.

Course 2


Vocabulary

indirect measurement

Insert Lesson Title Here

Course 2


Course 2


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


Check It Out: Example 1


Course 2


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.


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.


Course 2


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.


Additional Example 2: Measurement Application


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


Course 2


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.


?

Additional Example 3: Estimating with Indirect Measurement

Course 2


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.


Course 2


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.


Course 2


1.

2.

x = 120 cm

t = 150 cm

Lesson Quiz: Part II

Find the unknown length in each pair of similar figures.


Course 2


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

5-6

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