Preview Warm Up California Standards Lesson Presentation

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

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

Vocabulary indirect measurement

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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