5. 5% of $70 Warm Up Solve each proportion. 1. 2. 3. 4. x = 20 x = 45 Evaluate: ½ m2 when m = 6 3. 4. Twelve of the 28 student are boys. If the teacher calls on one student randomly, what is the probability a girl will be called on? 18 5. 5% of $70 $3.50 4/7

Learning Target: Find measures indirectly by applying the properties of similar figures.

Triangles ABC and EFG are similar. Find the length of side EG. 9 ft x B A C 3 ft 4 ft AB AC EF EG = 3 4 9 x = 3x = 36 x = 12 ft

Triangles DEF and GHI are similar. Find the length of side HI. x E D F 7 in 2 in

Understand the Problem Example 1: 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.

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

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 ft 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 On your Own 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 ______ • The height of the building is ________. • The length of the tree’s shadow is _________.

2 Make a Plan Use the information to draw a diagram.

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. 4 Look Back

Practice Set A) Trevor took big steps to find the length of the shadow of the big pine tree in front of the school. He estimated that the shadow was 16 yards long, or about 48 feet. He also stepped off the shadow cast by the two-story school building and estimated that its shadow was 18 feet long. Trevor thinks the building is 24 feet tall. About how many feet tall is the big pine tree?

B) Holding a ruler upright at arm’s distance (24 inches), Ronnie aligned the bottom of the ruler with a mark on the utility pole that was about 5 feet above the ground. He saw that the top of the pole aligned with the 6-inch mark on the ruler. Then he took 40 long strides to reach the pole. If each stride was about one yard (3 feet), then the top of the pole is about how many feet high?