Similar Figures5-5

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Similar Figures5-5

Weekly Agenda 9/23 - 9/27Monday – 5-5 Similar Figures NOTESTuesday – 5-5 Similar Figures Practice(Tutoring at 7 over 5-2 & 5-5)Wednesday – Quiz 5-2 & 5-5Thursday – 5-6 Dilations NOTESFriday – 5-6 Dilations Practice

Similar Figures5-5

Warm UpSolve each proportion.

b30

39

=1. 5635

y5

=2.

412

p9

=3. 56m

2826

=4.

b = 10 y = 8

p = 3 m = 52

Similar Figures5-5

Problem of the Day

A rectangle that is 10 in. wide and 8 in. long is the same shape as one that is 8 in. wide and x in. long. What is the length of the smaller rectangle?6.4 in.

Similar Figures5-5

Learn to determine whether figures are similar and to find missing dimensions in similar figures.

Similar Figures5-5

Vocabulary

similar

corresponding sides

corresponding angles

Similar Figures5-5

Similar figures have the same shape, but not necessarily the same size.

Corresponding sides of two figures are in the same relative position, and corresponding angles are in the same relative position. Two figures are similar if the lengths of corresponding sides are proportional and the corresponding angles have equal measures.

Similar Figures5-5

Similar Figures5-5

Additional Example 1: 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.

Similar Figures5-5

Additional Example 1 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. Therefore, rectangle K 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.

Similar Figures5-5

Check It Out: Example 1

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.

Similar Figures5-5

Check It Out: Example 1 Continued

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. Therefore, rectangle B 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.

Similar Figures5-5

14 ∙ 1.5 = w ∙ 10 Find the cross products.

Divide both sides by 10.10w10

2110

=

width of a picturewidth on Web page

height of picture height on Web page

14w

= 101.5

2.1 = w

Set up a proportion. Let w be the width of the picture on the Web page.

The picture on the Web page should be 2.1 in. wide.

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?

Additional Example 2: Finding Missing Measures in Similar Figures

21 = 10w

Similar Figures5-5

56 ∙ 10 = w ∙ 40 Find the cross products.

Divide both sides by 40.40w40

56040

=

width of a paintingwidth of poster

length of painting length of poster

56w

= 4010

14 = w

Set up a proportion. Let w be the width of the painting on the Poster.

The painting displayed on the poster should be 14 in. long.

Check It Out: Example 2

560 = 40w

A painting 40 in. long and 56 in. wide is to be scaled to 10 in. long to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar?

Similar Figures5-5

Additional Example 3: 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 • x = 3 • 6 Find the cross products.

Similar Figures5-5

4.5x = 18

x = = 4184.5

Multiply.

Solve for x.

Additional Example 3 Continued

The third side of the triangle is 4 ft long.

Similar Figures5-5

Check It Out: Example 3

Set up a proportion.24 ftx in.

18 ft4 in.

=

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

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?

Similar Figures5-5

18x = 96

x = 5.39618

Multiply.

Solve for x.

Check It Out: Example 3 Continued

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

Similar Figures5-5

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Similar Figures5-5

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. Leah 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?

17 in.

3.75 ft

A and B are similar.

Similar Figures5-5

1. A rectangular garden is 45 ft wide and 70 ft long. On a blueprint, the width is 9 in. Identify the length on the blueprint.

A. 7 in.

B. 9 in.

C. 12 in.

D. 14 in.

Lesson Quiz for Student Response Systems

Similar Figures5-5

2. Rob enlarged a 4 in. wide by 7 in. tall picture into a banner. If the banner is 3.5 ft wide, how tall is it?

A. 6.05 ft

B. 6.125 ft

C. 7 ft

D. 7.125 ft

Lesson Quiz for Student Response Systems

Similar Figures5-5

3. Which triangles are similar?

A. X and Y

B. X and Z

C. Y and Z

D. none

Lesson Quiz for Student Response Systems

X

Y

Z