Using similar figures
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1. This document is a lesson on using similar figures to find unknown lengths through indirect measurement using proportions. It includes examples of finding unknown side lengths of similar triangles and rectangles. 2. The lesson defines indirect measurement as using proportions to find unknown lengths or distances in similar figures. It provides examples of writing proportions and solving for unknown variables. 3. The examples demonstrate applications like estimating the height of a traffic light using similar triangles of known and unknown heights. Practice problems are included to find unknown side lengths in similar shapes.
Using similar figures
- 1. 5-8 Using Similar Figures Course 2 Warm UpWarm Up Problem of the DayProblem of the Day Lesson PresentationLesson Presentation
- 2. Course 2 5-8 Using Similar Figures Warm Up Solve each proportion. 1. k 4 = 75 25 2. 6 19 = 24 x 3. Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. J N Z K O A JN KO k = 12 x = 76
- 3. Problem of the Day Harvey starts to fill a 3-gallon tank from a hose that delivers 1 gallon per minute. However, the tanks leaks 1 quart per minute. In how many minutes will the tank begin to overflow? 4 Course 2 5-8 Using Similar Figures
- 4. Learn to use similar figures to find unknown lengths. Course 2 5-8 Using Similar Figures
- 5. Vocabulary indirect measurement Insert Lesson Title Here Course 2 5-8 Using Similar Figures
- 6. Course 2 5-8 Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.
- 7. Find the unknown length in similar figures. Additional Example 1: Finding Unknown Lengths in Similar Figures AC QS = AB QR Write a proportion using corresponding sides. 12 48 = 14 w Substitute lengths of the sides. 12 · w = 48 · 14 Find the cross product. 12w = 672 Multiply. 12w 12 = 672 12 w = 56 QR is 56 centimeters. Divide each side by 12 to isolate the variable. Course 2 5-8 Using Similar Figures
- 8. Check It Out: Example 1 Insert Lesson Title Here Course 2 5-8 Using Similar Figures A B C D 10 cm 12 cm Q R S T 24 cm AC QS = AB QR Write a proportion using corresponding sides. 12 24 = 10 x Substitute lengths of the sides. 12 · x = 24 · 10 Find the cross product. 12x = 240 Multiply. 12x 12 = 240 12 x = 20 QR is 20 centimeters. Divide each side by 12 to isolate the variable. Find the unknown length in similar figures. x
- 9. The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle. Insert Lesson Title Here Course 2 5-8 Using Similar Figures Let x = the base of the inside triangle. 8 2 =12 x 8 · x = 2 · 12 8x = 24 8x 8 = 24 8 x = 3 The base of the inside triangle is 3 inches. Write a proportion using corresponding side lengths. Find the cross products. Multiply. Divide each side by 8 to isolate the variable. Additional Example 2: Measurement Application
- 10. Check It Out: Example 2 The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle. Insert Lesson Title Here Course 2 5-8 Using Similar Figures 3 cm 6 cm 12 cm Let w = the width of the right rectangle. 6 12 = 3 w 6 ·w = 12 · 3 6w = 36 6w 6 = 36 6 w = 6 The right rectangle is 6 cm wide. Write a proportion using corresponding side lengths. Find the cross products. Multiply. Divide each side by 6 to isolate the variable. ?
- 11. Additional Example 3: Estimating with Indirect Measurement Course 2 5-8 Using Similar Figures City officials want to know the height of a traffic light. Estimate the height of the traffic light. 27.25 15 = 48.75 h Write a proportion. Use compatible numbers to estimate. 9 5 ≈ 49 h Simplify. 9h ≈ 245 The traffic light is about 30 feet tall. 27.25 ft 48.75 ft h ft 27 15 ≈ 49 h Cross multiply. h ≈ 27 Multiply each side by 9 to isolate the variable.
- 12. Check It Out: Example 3 Course 2 5-8 Using Similar Figures The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle. 5 14.75 = h 30.25 Write a proportion. Use compatible numbers to estimate. 1 3 ≈ h 30 Simplify. 1 • 30 ≈ 3 • h The outside triangle is about 10 feet tall. 14.75 ft 30.25 ft h ft 5 15 ≈ h 30 30 ≈ 3h Multiply each side by 5 to isolate the variable. 5 ft Cross multiply. 10 ≈ h
- 13. Lesson Quiz: Part I Find the unknown length in each pair of similar figures. Insert Lesson Title Here Course 2 5-8 Using Similar Figures 1. 2. x = 120 cm t = 150 cm
- 14. Lesson Quiz: Part II Find the unknown length in each pair of similar figures. Insert Lesson Title Here Course 2 5-8 Using Similar Figures 3. The width of the smaller rectangular cake is 5.75 in. The width of a larger rectangular cake is 9.25 in. Estimate the length of the larger rectangular cake. x = 15 inches