Warm Up Solve each proportion

Students will be able to determine whether figures are similar and find missing dimensions in similar figures.5-5

Warm UpSolve each proportion.

b30

39 =1. 56

35y5 =2.

3.

4.

b = 10 y = 8

8 girls and 16 boys

20

There are 24 students in Juan’s class. The ratio of girls to boys is 1:2. How many girls and boys are in Juan’s class?

Three are 32 green and purple markers in a box. The ratio of green markers to purple markers is 3:5. How many of the markers are purple?


Homework Review


Daily Quiz1. Tim can decorate 3 T-shirts in 20 minutes.

How many T-shirts can he decorate in 180 minutes?

2. A company produced blue T-shirts and red T-shirts in the ratio of 22:8. In one hour, the company produced 120 red T-shirts. How many blue T-shirts did the company produce in that hour?

27

330


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


Corresponding sides & Corresponding angles

A

p and br and cq and a

Q and AR and CP and B

Sides or angles in the same position on each triangle. Example:


For two polygons to be similar:

1. Corresponding angles must have the same measures.

2. The ratios of the lengths of the corresponding sides must be proportional.


Proportions the same.

Angles the same.

Size NOT the same.

Example of similar figures.

http://www.mylot.com/w/image/462387.aspx


New Ferrari V4 Motorcycle Concept designed by Amir GlinkPacked with a modified engine from a Ferrari Enzo! The hand controls are from a F-16 fighter jet Buttons are from a Forumla 1 race car



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.


Additional Example 1 Continued

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

20 = 20

length of rectangle Jlength of rectangle K

width of rectangle Jwidth of rectangle K

10 5

42

? =

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



50 48The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to rectangle L.

length of rectangle Jlength of rectangle L

width of rectangle Jwidth of rectangle L

1012

45

?=


Try It: 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.


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.


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 = 10

1.5

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


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 = 40

10

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?


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.


4.5x = 18

x = = 4184.5

Multiply.

Solve for x.


The third side of the triangle is 4 ft long.


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?


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.


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?

17 in.

3.75 ft

A and B are similar.


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


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



3. Which triangles are similar? A. X and Y

B. X and Z

C. Y and Z

D. none


X

Y

Z

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Warm Up Solve each proportion