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Similar Figures 4-3 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.

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Similar Figures 4-3 Learn to determine whether figures are similar and to find missing dimensions in similar figures.

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Similar Figures 4-3 Vocabulary similar corresponding sides corresponding angles

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Similar Figures 4-3 Similar figures have the same shape, but not necessarily the same size. Corresponding sides and corresponding angles of two figures 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.

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Similar Figures 4-3

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Similar Figures 4-3 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.

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Similar Figures 4-3 Additional Example 1 Continued 50 48 The notation J ~ K shows similarity. The ratios are not equal. Rectangle K is not similar to rectangle L. 20 = 20 length of rectangle J length of rectangle K width of rectangle J width of rectangle K 10 5 4242 ? = length of rectangle J length of rectangle L width of rectangle J width of rectangle L 10 12 4545 ? = Compare the ratios of corresponding sides to see if they are equal.

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Similar Figures 4-3 Check It Out: 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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Similar Figures 4-3 Check It Out: Example 1 Continued 16 20 A ~ B 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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Similar Figures 4-3 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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Similar Figures 4-3 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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Similar Figures 4-3 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.

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Similar Figures 4-3 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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Similar Figures 4-3 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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Similar Figures 4-3 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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Similar Figures 4-3 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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