Pre-Algebra

7-6 Similar Figures7-6 Similar Figures

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-6 Similar Figures

Warm UpSolve each proportion.

Pre-Algebra

7-6 Similar Figures

b30

39

=1. 5635

y5

=2.

412

p9

=3. 56m

2826

=4.

b = 10 y = 8

p = 3 m = 52

Pre-Algebra

7-6 Similar Figures

Problem of the Day

A plane figure is dilated and gets 50% larger. What scale factor should you use to dilate the figure back to its original size? (Hint: The answer is not ).1

223

Pre-Algebra

7-6 Similar Figures

Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions in similar figures.

Pre-Algebra

7-6 Similar Figures

Vocabulary

similar

Pre-Algebra

7-6 Similar Figures

The heights of letters in newspapers and on billboards are measured using points and picas. There are 12 points in 1 pica and 6 picas in one inch.

A letter 36 inches tall on a billboard would be 216 picas, or 2592 points. The first letter in this paragraph is 12 points.

Pre-Algebra

7-6 Similar Figures

Congruent figures have the same size and shape. Similar figures have the same shape, but not necessarily the same size. The A’s in the table are similar. The have the same shape, but they are not the same size.

The ratio formed by the corresponding sides is the scale factor.

Pre-Algebra

7-6 Similar Figures

Additional Example 1: Using Scale Factors to Find Missing Dimensions

A picture 10 in. tall and 14 in. wide is to be scaled to 1.5 in. tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar?To find the scale factor, divide the known measurement of the scaled picture by the corresponding measurement of the original picture.

0.15 0.151.510

=

Then multiply the width of the original picture by the scale factor.2.1 14 • 0.15 = 2.1

The picture should be 2.1 in. wide.

Pre-Algebra

7-6 Similar Figures

Try This: Example 1

A painting 40 in. tall and 56 in. wide is to be scaled to 10 in. tall to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar?To find the scale factor, divide the known measurement of the scaled painting by the corresponding measurement of the original painting.0.25 0.2510

40=

Then multiply the width of the original painting by the scale factor.14 56 • 0.25 = 14

The painting should be 14 in. wide.

Pre-Algebra

7-6 Similar Figures

Additional Example 2: Using Equivalent Ratios to Find Missing Dimensions

A T-shirt design includes an isosceles triangle with side lengths 4.5 in, 4.5 in., and 6 in. An advertisement shows an enlarged version of the triangle with two sides that are each 3 ft. long. What is the length of the third side of the triangle in the advertisement?

Set up a proportion.

6 in.x ft

4.5 in.3 ft

=

4.5 in. • x ft = 3 ft • 6 in. Find the cross products.

4.5 in. • x ft = 3 ft • 6 in. in. • ft is on both sides

Pre-Algebra

7-6 Similar Figures

4.5x = 3 • 6

4.5x = 18

x = = 4184.5

Cancel the units.

Multiply

Solve for x.

Additional Example 2 Continued

The third side of the triangle is 4 ft long.

Pre-Algebra

7-6 Similar Figures

Try This: Example 2

Set up a proportion.

24 ftx in.

18 ft4 in.

=

18 ft • x in. = 24 ft • 4 in. Find the cross products.

18 ft • x in. = 24 ft • 4 in. in • ft is on both sides

A flag in the shape of an isosceles triangle with side lengths 18 ft, 18 ft, and 24 ft is hanging on a pole outside a campground. A camp t-shirt shows a smaller version of the triangle with two sides that are each 4 in. long. What is the length of the third side of the triangle on the t-shirt?

Pre-Algebra

7-6 Similar Figures

18x = 24 • 4

18x = 96

x = 5.39618

Cancel the units.

Multiply

Solve for x.

Try This: Example 2 Continued

The third side of the triangle is about 5.3 in. long.

Pre-Algebra

7-6 Similar Figures

The following are matching, or corresponding:A and X

Remember!

AB and XY

BC and YZ

AC and XZ

A

C BZ Y

X

C and Z

B and Y

Pre-Algebra

7-6 Similar Figures

Additional Example 3: Identifying Similar Figures

Which rectangles are similar?

Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

Pre-Algebra

7-6 Similar Figures

Additional Example 3 Continued

50 48

The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity.

The ratios are not equal. Rectangle J is not similar to rectangle L.

20 = 20

length of rectangle Jlength of rectangle K

width of rectangle Jwidth of rectangle K

10 5

42

? =

length of rectangle Jlength of rectangle L

width of rectangle Jwidth of rectangle L

1012

45

?=

Compare the ratios of corresponding sides to see if they are equal.

Pre-Algebra

7-6 Similar Figures

Try This: Example 3

Which rectangles are similar?

A8 ft

4 ft

B6 ft

3 ft

C5 ft

2 ft

Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

Pre-Algebra

7-6 Similar Figures

Try This: Example 3

16 20

The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity.

The ratios are not equal. Rectangle A is not similar to rectangle C.

24 = 24

length of rectangle Alength of rectangle B

width of rectangle Awidth of rectangle B

8 6

43

? =

length of rectangle Alength of rectangle C

width of rectangle Awidth of rectangle C

8 5

42

?=

Compare the ratios of corresponding sides to see if they are equal.

Pre-Algebra

7-6 Similar Figures

Lesson QuizUse the properties of similar figures to answer each question.

1. A rectangular house is 32 ft wide and 68 ft long. On a blueprint, the width is 8 in. Find the length on the blueprint.

2. Karen enlarged a 3 in. wide by 5 in. tall photo into a poster. If the poster is 2.25 ft wide, how tall is it?

3. Which rectangles are similar?