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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 9 27. 3 5. 6 x. x 75. 2.4 8. x 6. =. =. =. Warm Up Solve each proportion. 1. 2. x = 45. x = 20. x 3.5. 8 7. 3. 4. x = 4. =. x = 2. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 927 3 5 6 x x 75 2.4 8 x 6 = = = Warm Up Solve each proportion. 1. 2. x = 45 x = 20 x 3.5 8 7 3. 4. x = 4 = x = 2

  3. California Standards Extension of MG1.2 Construct and read drawings and models made to scale.

  4. Vocabulary indirect measurement

  5. Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

  6. F B 9 ft 3 ft A C 4 ft G E x Additional Example 1: Geography Application Triangles ABC and EFG are similar. Find the length of side EG. Triangles ABC and EFG are similar.

  7. 36 EF 9 EG x 3 AB 3x 3 4 3 AC Additional Example 1 Continued Triangles ABC and EFG are similar. Find the length of side EG. = Set up a proportion. Substitute 3 for AB, 4 for AC, and 9 for EF. = 3x = 36 Find the cross products. = Divide both sides by 3. x = 12 The length of side EG is 12 ft.

  8. H x E 7 in 8 in D F I G Check It Out! Example 1 Triangles DEF and GHI are similar. Find the length of side HI. 2 in Triangles DEF and GHI are similar.

  9. GH 56 8 2 HI x DE 2x 2 2 7 EF Check It Out! Example 1 Continued Triangles DEF and GHI are similar. Find the length of side HI. = Set up a proportion. Substitute 2 for DE, 7 for EF, and 8 for GH. = 2x = 56 Find the cross products. = Divide both sides by 2. x = 28 The length of side HI is 28 in.

  10. 1 Understand the Problem Additional Example 2: Problem Solving Application A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree? The answer is the height of the tree. List theimportant information: • The length of the building’s shadow is 75 ft. • The height of the building is 30 ft. • The length of the tree’s shadow is 35 ft.

  11. 3 Solve Make a Plan h 30 feet 35 feet 75 feet 2 Additional Example 2 Continued Use the information to draw a diagram. Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

  12. 3 Solve 1050 75 75h 75 Additional Example 2 Continued 30 75 h 35 Corresponding sides of similar figures are proportional. = 75h = 1050 Find the cross products. = Divide both sides by 75. h = 14 The height of the tree is 14 feet.

  13. 4 Additional Example 2 Continued Look Back 75 30 Since = 2.5, the building’s shadow is 2.5 times its height. So, the tree’s shadow should also be 2.5 times its height and 2.5 of 14 is 35 feet.

  14. 1 Understand the Problem Check It Out! Example 2 A 24-ft building casts a shadow that is 8 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree? The answer is the height of the tree. List theimportant information: • The length of the building’s shadow is 8 ft. • The height of the building is 24 ft. • The length of the tree’s shadow is 3 ft.

  15. 3 Solve Make a Plan h 24 feet 3 feet 8 feet 2 Check It Out! Example 2 Continued Use the information to draw a diagram. Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

  16. 3 Solve 8h 8 72 8 Check It Out! Example 2 Continued 24 8 h 3 Corresponding sides of similar figures are proportional. = 72 = 8h Find the cross products. = Divide both sides by 8. 9 = h The height of the tree is 9 feet.

  17. 4 Check It Out! Example 2 Continued Look Back 8 24 1 3 Since = , the building’s shadow is times its height. So, the tree’s shadow should also be times its height and of 9 is 3 feet. 1 3 1 3 1 3

  18. w 5 m 7 m 5.7 m Lesson Quiz 1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river? 2. A yardstick casts a 2 ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree? 7.98 m 9 ft

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