PPT 5-7 Similar Figures - PMS-Math

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Transcript PPT 5-7 Similar Figures - PMS-Math

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

Warm Up Solve each proportion.

1.

3 9 =

b

b = 10

2. y

5 = 56 35

y = 8

3.

There are 24 students in Juan’s class. The ratio are in Juan’s class?

8 girls and 16 boys

4.

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?

20

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

Homework Review

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

Daily Quiz

1. Tim can decorate 3 T-shirts in 20 minutes. How many T-shirts can he decorate in 180 minutes?

27 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?

330

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

Learn

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

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

Corresponding sides & Corresponding angles

Sides or angles in the same position on each triangle. Example: p and b r and c q and a A Q and A R and C P and B

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

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.

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

Example of similar figures.

Proportions the same.

Angles the same.

Size NOT the same.

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

New Ferrari V4 Motorcycle Concept designed by Amir Glink Packed 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

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

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.

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

Additional Example 1 Continued

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

length of rectangle J length of rectangle K 10 5 4 2 20 = 20 width of rectangle J width of rectangle K The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity.

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

Additional Example 1 Continued

length of rectangle J length of rectangle L 10 12 4 5 width of rectangle J width of rectangle L rectangle L. 50  48 The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to

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

Try It: Example 1 Which rectangles are similar?

8 ft

4 ft 6 ft

3 ft 5 ft

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

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

Check It Out: Example 1 Continued

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

length of rectangle A length of rectangle B 8 6 4 3 24 = 24 width of rectangle A width of rectangle B The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity.

length of rectangle A length of rectangle C 8 5 4 2 width of rectangle A width of rectangle C 16  20 The ratios are not equal. Rectangle A is not similar to rectangle C. Therefore, rectangle B is not similar to rectangle C.

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

Additional Example 2: Finding Missing Measures in Similar Figures 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?

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

width of a picture width on Web page

w height of picture height on Web page

14 ∙ 1.5 = w ∙ 10

Find the cross products.

21 = 10w 21 10 = 10w 10

Divide both sides by 10.

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

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

Check It Out: Example 2 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?

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

width of a painting width of poster

w length of painting length of poster Find the cross products.

56 ∙ 10 = w ∙ 40 560 = 40w 560 40 = 40w 40 14 = w

Divide both sides by 40.

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

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

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?

4.5 in.

3 ft = 6 in.

x ft

4.5 • x = 3 • 6

Set up a proportion.

Find the cross products.

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

Additional Example 3 Continued

4.5x = 18

Multiply.

Solve for x.

The third side of the triangle is 4 ft long.

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

Check It Out: Example 3 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?

18 ft 4 in.

= 24 ft

x in.

18 • x = 24 • 4

Set up a proportion.

Find the cross products.

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

Check It Out: Example 3 Continued

18x = 96

x =

 5.3

Multiply.

Solve for x.

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

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

each question.

Lesson Quiz Use the properties of similar figures to answer

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.

17 in.

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?

3.75 ft

3. Which rectangles are similar?

A and B are similar.

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

Lesson Quiz for Student Response Systems

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.

9 in.

12 in.

14 in.

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

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?

6.05 ft B. 6.125 ft

7 ft

7.125 ft

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

Lesson Quiz for Student Response Systems

3. Which triangles are similar?

X and Y

B. X and Z

C. Y and Z

none