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Preparation for MG1.2 Construct and read drawings and models made to scale.

California Standards. Preparation for MG1.2 Construct and read drawings and models made to scale. Similar figures have the same shape, but not necessarily the same size.

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Preparation for MG1.2 Construct and read drawings and models made to scale.

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  1. California Standards Preparation for MG1.2 Construct and read drawings and models made to scale.

  2. 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.

  3. 43° 43°

  4. Reading Math A is read as “angle A.” ∆ABC is read as “triangle ABC.” “∆ABC ~∆EFG” is read as “triangle ABC is similar to triangle EFG.”

  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.

  6. length of rectangle J length of rectangle K 10 5 4 2 width of rectangle J width of rectangle K ? = length of rectangle J length of rectangle L 10 12 4 5 width of rectangle J width of rectangle L ? = Additional Example 1 Continued Compare the ratios of corresponding sides to see if they are equal. 20 = 20 The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity. 50  48 The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to rectangle L.

  7. Check It Out! Example 1 Which rectangles are similar? 8 ft A 6 ft B C 5 ft 4 ft 3 ft 2 ft Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

  8. length of rectangle A length of rectangle B 8 6 4 3 width of rectangle A width of rectangle B ? = length of rectangle A length of rectangle C 8 5 4 2 width of rectangle A width of rectangle C ? = Check It Out! Example 1 Continued Compare the ratios of corresponding sides to see if they are equal. 24 = 24 The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity. 16  20 The ratios are not equal. Rectangle A is not similar to rectangle C. Therefore, rectangle B is not similar to rectangle C.

  9. width of a picture width on Web page height of picture height on Web page 14 w 10 1.5 = 21 10 10w 10 = 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. 14 ∙ 1.5 = w ∙ 10 Find the cross products. 21 = 10w Divide both sides by 10. 2.1 = w The picture on the Web page should be 2.1 in. wide.

  10. width of a painting width of poster length of painting length of poster 56 w 40 10 = 560 40 40w 40 = 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. 56 ∙ 10 = w ∙ 40 Find the cross products. 560 = 40w Divide both sides by 40. 14 = w The painting displayed on the poster should be 14 in. long.

  11. side of small triangle base of small triangle side of large triangle base of large triangle = 4.5 in. 6 in. 3 ft x ft = Additional Example 3: Business Application 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. Find the cross products. 4.5 • x = 3 • 6 Multiply. 4.5x = 18

  12. 18 4.5 x = = 4 Additional Example 3 Continued 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? Solve for x. The third side of the triangle is 4 ft long.

  13. side of large triangle side of small triangle base of large triangle base of small triangle = 18 ft 4 in. 24 ft x in. = 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? Set up a proportion. 18 ft • x in. = 24 ft • 4 in. Find the cross products. Multiply. 18x = 96

  14. 96 18 x =  5.3 Check It Out! Example 3 Continued 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? Solve for x. The third side of the triangle is about 5.3 in. long.

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