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Preview Warm Up California Standards Lesson Presentation

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**Warm Up Solve each proportion. = = 1. 2. = 3. 4. = x 75 3 5 2.4 8 6 x**

9 27 = x 3.5 8 7 3. 4. = x = 4 x = 2

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**Extension of MG1.2 Construct and read drawings and models made to scale.**

California Standards

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Vocabulary indirect measurement

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**Sometimes, distances cannot be measured directly**

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.

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**Additional Example 1: Geography Application**

Triangles ABC and EFG are similar. Find the length of side EG. F E G 9 ft x B A C 3 ft 4 ft Triangles ABC and EFG are similar.

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**Additional Example 1 Continued**

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

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**Triangles DEF and GHI are similar. Find the length of side HI.**

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

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**Check It Out! Example 1 Continued**

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

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**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? 1 Understand the Problem The answer is the height of the tree. List the important 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.

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**Additional Example 2 Continued**

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

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**Additional Example 2 Continued**

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

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**Additional Example 2 Continued**

4 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.

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**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? 1 Understand the Problem The answer is the height of the tree. List the important 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.

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**Check It Out! Example 2 Continued**

Make a Plan Use the information to draw a diagram. h 3 feet 8 feet 24 feet Solve 3 Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

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**Check It Out! Example 2 Continued**

Solve 3 24 8 h 3 Corresponding sides of similar figures are proportional. = 72 = 8h Find the cross products. 72 8 8h 8 = Divide both sides by 8. 9 = h The height of the tree is 9 feet.

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**Check It Out! Example 2 Continued**

4 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

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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 w 7 m 5 m 5.7 m 9 ft

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