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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Warm Up Solve each proportion. b 30 3939 = 1. 56 35 y5y5 = 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?

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

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Daily Quiz 1.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

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

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Corresponding sides & Corresponding angles A p and b r and c q and a Q and A R and C P and B Sides or angles in the same position on each triangle. Example:

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

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Proportions the same. Angles the same. Size NOT the same. Example of similar figures.

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

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

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

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 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 J length of rectangle K width of rectangle J width of rectangle K 10 5 4242 ? = Compare the ratios of corresponding sides to see if they are equal.

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Additional Example 1 Continued 50 48 The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to rectangle L. length of rectangle J length of rectangle L width of rectangle J width of rectangle L 10 12 4545 ? =

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Try It: Example 1 Which rectangles are similar? A 8 ft 4 ft B6 ft 3 ft C 5 ft 2 ft Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 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 A length of rectangle B width of rectangle A width of rectangle B 8 6 4343 ? = length of rectangle A length of rectangle C width of rectangle A width of rectangle C 8 5 4242 ? = Compare the ratios of corresponding sides to see if they are equal.

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 14 ∙ 1.5 = w ∙ 10Find the cross products. Divide both sides by 10. 10w 10 21 10 = width of a picture width on Web page height of picture height on Web page 14 w = 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

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 56 ∙ 10 = w ∙ 40Find the cross products. Divide both sides by 40. 40w 40 560 40 = width of a painting width of poster length of painting length of poster 56 w = 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?

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

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 4.5x = 18 x = = 4 18 4.5 Multiply. Solve for x. Additional Example 3 Continued The third side of the triangle is 4 ft long.

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 Check It Out: Example 3 Set up a proportion. 24 ft x in. 18 ft 4 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?

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Students will be able to determine whether figures are similar and find missing dimensions in similar figures. 5-5 18x = 96 x = 5.3 96 18 Multiply. Solve for x. Check It Out: Example 3 Continued The third side of the triangle is about 5.3 in. long.

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

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

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

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

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