8-5 Indirect Measurement Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up Find the missing value in each proportion. 1. = 2. = 3. = 4. = t = 15 k = 5 n = 56 Course Indirect Measurement 6 t __ __ k 19 __ __ n __ __ x 44 __ x = 84

Problem of the Day Bryce, Kate, and Annie have drawn rectangles. Each side of Bryce’s rectangle is twice the size of one side of Kate’s. The same side of Kate’s rectangle is congruent to one side of Annie’s. One side of Annie’s rectangle is congruent to one side of Bryce’s. Which two rectangles could be congruent? Kate’s and Annie’s Course Indirect Measurement

Learn to use proportions and similar figures to find unknown measures. Course Indirect Measurement

Vocabulary indirect measurement Insert Lesson Title Here Course Indirect Measurement

Course Indirect Measurement One way to find a height that you cannot measure directly is to use similar figures and proportions. This method is called indirect measurement.

Course Indirect Measurement Additional Example 1: Using Indirect Measurement Use the similar triangles to find the height of the tree. 2 7 __ 6 h = h 2 = 6 7 2h = 42 2h 2 ___ 42 2 ___ = h = 21 Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 2. Divide both sides by 2 to undo multiplication. The tree is 21 feet tall.

Course Indirect Measurement Try This: Example 1 Use the similar triangles to find the height of the tree. 3 9 __ 6 h = h 3 = 6 9 3h = 54 3h 3 ___ 54 3 ___ = h = 18 Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 3. Divide both sides by 3 to undo multiplication. The tree is 18 feet tall. 3 ft. 9 ft. 6 ft. h

Course Indirect Measurement Additional Example 2: Measurement Application A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket? ____ h 4 __ = = h = 3h ___ 3h 3 ___ = 122 = h Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 3. Divide both sides by 3 to undo multiplication. The rocket is 122 feet tall.

Course Indirect Measurement Try This: Example 2 A building casts a shadow that is 72.5 feet long when a 4-foot model building casts a shadow that is 2 feet long. How tall is the building? ____ h 4 __ = = h = 2h ___ 2h 2 ___ = 145 = h Write a proportion using corresponding sides. The cross products are equal. h is multiplied by 2. Divide both sides by 2 to undo multiplication. The building is 145 feet tall. h 72.5 ft 2 ft 4 ft

Lesson Quiz 1. On a sunny day, a telephone pole casts a shadow 21 ft long. A 5-foot-tall mailbox next to the pole casts a shadow 3 ft long. How tall is the pole? 2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost? 25 feet 35 feet Insert Lesson Title Here Course Indirect Measurement