Cgpe-0700 8/16/01 9:51 AM Page 354 Chapter 7 ...

7 CChhaapptteerr

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How does a drawing become a mural?

Murals are often created by enlarging an original drawing. People use projection machines, grids, and other methods to make sure that all parts of a mural are in proportion to the original drawing.

original figure

enlarged figure

Learn More About It

You will learn more about enlarging drawings in Exercise 21 on p. 370.

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Who uses

Similarity?

MAP MAKER Map makers analyze photographs, satellite images, and other data to create maps. Maps may be designed for travel, tourism, weather forecasting, and geological exploration. (p. 360)

ARTIST Painters, photographers, sculptors, and muralists use proportions to enlarge and reduce the size of an original art piece. Proportions are also used to draw human figures and make perspective drawings. (p. 370)

How will you use these ideas?

? Estimate distances on a map. (p. 360) ? Compare the dimensions of television screens. (p. 371) ? Analyze a hockey pass. (p. 374) ? Calculate the height of a flag pole. (p. 377) ? See how similarity appears in fractals. (p. 391)

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7 Chapter

Study Guide

PREVIEW

What's the chapter about?

? Using ratios and proportions ? Identifying similar polygons and showing that triangles are similar ? Identifying and drawing dilations

Key Words

? ratio of a to b, p. 357 ? proportion, p. 359 ? similar polygons, p. 365

? scale factor, p. 366 ? midsegment of a triangle, p. 389 ? dilation, p. 393

PREPARE

Chapter Readiness Quiz

Take this quick quiz. If you are unsure of an answer, look at the reference pages for help.

Vocabulary Check (refer to pp. 234, 241)

J

P

1. Which congruence statement is correct

for the triangles at the right?

L

KR

P

A TLKJ c TQRP

B TJLK c TPQR

C TLJK c TRPQ

D TKLJ c TQPR

Skill Check (refer to pp. 333, 656)

2. What is the value of x?

3

F 4

G 5

x

H 5.5

J 6

7

3. Which of the following fractions can be simplified to 27?

A 188

B 261

C 1228

D 3183

VISUAL STRATEGY Visualize It!

Separating Triangles

To help you see triangle relationships more clearly, sketch overlapping triangles separately and label them with their measures.

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Chapter 7 Similarity

A

23

D

E

4

6

B

C

A 23

A

DE

6

B

9 C

7.1 Ratio and Proportion

Goal

Use ratios and proportions.

Key Words

? ratio of a to b ? proportion ? means ? extremes

In 2000, Nomar Garciaparra of the Boston Red Sox won the American League batting title for the second straight year, with a batting average of .372. He was at bat 529 times and had 197 hits. A baseball player's batting average is calculated using a ratio.

timehsi tast bat 159279 0.372

A ratio is a comparison of a number a and a nonzero number b using division.

The ratio of a to b can be written in three ways: as the fraction ab (or an equivalent decimal), as a : b, or as "a to b." A ratio is usually written in simplest form.

Student Help

STUDY TIP Before you simplify a ratio, make sure that the quantities in the numerator and denominator are measured in the same units.

EXAMPLE 1 Simplify Ratios

Simplify the ratio. a. 60 cm : 200 cm

b. 183 ifnt .

Solution a. 60 cm : 200 cm can be written as the fraction 26000c cmm.

26000c cmm 26000 2200 130

Divide numerator and denominator by their greatest common factor, 20.

Simplify. 130 is read as "3 to 10."

b. 138 fint . 3 p1812 ini.n. 3168 iinn.. 1386 1188 21

Substitute 12 in. for 1 ft.

Multiply. Divide numerator and denominator by their greatest common factor, 18. Simplify. 21 is read as "2 to 1."

7.1 Ratio and Proportion 357

Student Help

SKILLS REVIEW To review the formula for the perimeter of a rectangle, see p. 674.

EXAMPLE 2 Use Ratios

In the diagram, AB : BC is 4 : 1 and AC 30. Find AB and BC.

A

Solution

Let x BC. Because the ratio of AB to BC

is 4 to 1, you know that AB 4x.

A

30 4x

AB BC AC 4x x 30 5x 30 x6

Segment Addition Postulate Substitute 4x for AB, x for BC, and 30 for AC. Add like terms. Divide each side by 5.

To find AB and BC, substitute 6 for x.

AB 4x 4 p 6 24

BC x 6

ANSWER So, AB 24 and BC 6.

BC

x BC

EXAMPLE 3 Use Ratios

The perimeter of a rectangle is 80 feet. The ratio of the length to the width is 7 : 3. Find the length and the width of the rectangle.

Solution

The ratio of length to width is 7 to 3. You can let the length l 7x and the width w 3x.

3x 7x

2l 2w P 2(7x) 2(3x) 80

14x 6x 80 20x 80 x4

Formula for the perimeter of a rectangle Substitute 7x for l, 3x for w, and 80 for P. Multiply. Add like terms. Divide each side by 20.

To find the length and width of the rectangle, substitute 4 for x.

l 7x 7 p 4 28

w 3x 3 p 4 12

ANSWER The length is 28 feet, and the width is 12 feet.

Use Ratios

1. In the diagram, EF : FG is 2 : 1 and EG 24. Find EF and FG.

24

E

F

G

2. The perimeter of a rectangle is 84 feet. The ratio of the length to the width is 4 : 3. Find the length and the width of the rectangle.

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Chapter 7 Similarity

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