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Mastering Indirect Measurement: Proportion and Similar Figures

Dive into the world of indirect measurement with this course. Learn how to find unknown measures using proportions and similar figures. Practice with engaging problems and examples to enhance your skills in this key mathematical concept.

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Mastering Indirect Measurement: Proportion and Similar Figures

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

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

  3. 8-5 Indirect Measurement Course 1 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

  4. 8-5 Indirect Measurement Course 1 Learn to use proportions and similar figures to find unknown measures.

  5. 8-5 Indirect Measurement Course 1 Insert Lesson Title Here Vocabulary indirect measurement

  6. 8-5 Indirect Measurement Course 1 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. 8-5 Indirect Measurement 2 6 42 2h __ __ ___ ___ 2 h 2 7 Course 1 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. 8-5 Indirect Measurement 3h 3 6 54 ___ __ __ ___ 3 3 9 h Course 1 Try This: 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. 8-5 Indirect Measurement 91.5 h 3h 366 __ ____ ___ ___ 3 4 3 3 Course 1 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. 8-5 Indirect Measurement 72.5 h 2h 290 ___ ____ __ ___ 2 2 4 2 Course 1 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? 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. h = 4 ft 145 = h 72.5 ft 2 ft The building is 145 feet tall.

  11. 8-5 Indirect Measurement Course 1 Insert Lesson Title Here 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? 35 feet 25 feet

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