Warm Up

1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2. 6 18 __ __ t 45 k 20 __ __ 19 76 6 42 __ __ 8 n 21 x __ __ 11 44 Warm Up Find the missing value in each proportion. 1. = 2. = 3. = 4. = t = 15 k = 5 n = 56 x = 84

3. 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? Annie’s and Kate’s

4. Learn to use proportions and similar figures to find unknown measures.

5. Vocabulary indirect measurement

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

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

8. 6 3 __ __ h 9 3h 54 ___ ___ 3 3 Check It Out: Example 1 Use the similar triangles to find the height of the tree. Write a proportion using corresponding sides. = h • 3= 6 • 9 The cross products are equal. 3h= 54 h is multiplied by 3. 6 ft. h Divide both sides by 3 to undo multiplication. = 3 ft. 9 ft. h = 18 The tree is 18 feet tall.

9. h 91.5 __ ____ 4 3 366 3h ___ ___ 3 3 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? Write a proportion using corresponding sides. = 4 • 91.5= h• 3 The cross products are equal. 366= 3h h is multiplied by 3. Divide both sides by 3 to undo multiplication. = 122 = h The rocket is 122 feet tall.

10. h 72.5 __ ____ 4 2 290 2h ___ ___ h 2 2 4 ft 72.5 ft 2 ft Check It Out: 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? Write a proportion using corresponding sides. = 4 • 72.5= h• 2 The cross products are equal. 290= 2h h is multiplied by 2. Divide both sides by 2 to undo multiplication. = 145 = h The building is 145 feet tall.

11. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

12. x 8 ft 15 ft 6 ft Lesson Quiz 1. Use the similar triangles to find the height of the post. 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? 20 feet 25 feet

13. x 5 ft 16 ft 4 ft Lesson Quiz for Student Response Systems 1. Use the similar triangles to identify the height of the telephone pole. A. 18 ft B. 20 ft C. 25 ft D. 27 ft

14. Lesson Quiz for Student Response Systems 2. On a sunny afternoon, a tree casts a 120-foot shadow. A 6-foot man beside the tree has a shadow 36 feet long. How tall is the tree? A. 20 ft B. 30 ft C. 36 ft D. 60 ft