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Lesson Presentation

This lesson focuses on solving problems involving similar figures through the method of indirect measurement. Students will learn to use proportions to find unknown lengths or distances in similar triangles. The lesson includes several examples where unknown measures are calculated using corresponding side lengths and angles. By applying these principles, learners will hone their skills in solving real-world problems related to geometry and measurement effectively.

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Lesson Presentation

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Presentation Transcript

  1. Lesson Presentation

  2. Sunshine State Standards MA.7.A.1.3 Solve problems involving similar figures. AlsoMA.7.A.1.1.

  3. Vocabulary indirect measurement

  4. Indirect measurementis a method of using proportions to find an unknown length or distance in similar figures.

  5. Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown measures in the similar figures. H B A 31° 10 cm y 5.8 cm x 6 cm 116 cm 59° J G 5 cm C AB JG BC HG = Write a proportion using corresponding sides. 6 x 10 5 = Substitute lengths of the sides. 10 · x= 5 · 6 Find the cross product. Multiply. 10x = 30 30 10 10x 10 = Divide each side by 12 to isolate the variable. x = 3 HG is 3 centimeters.

  6. Additional Example 1 Continued Find the unknown measures in the similar figures. H B A 31° 10 cm y 5.8 cm x 6 cm 116 cm 59° J G 5 cm C Step 2 Find y. Corresponding angles of similar triangles have equal angle measures. H corresponds to C y = 59

  7. Check It Out: Example 1 Find the unknown measures in the similar figures. D B A 27° 14 cm y 5.8 cm x 9 cm 116 cm 63° F E 7 cm C AB FE BC DE = Write a proportion using corresponding sides. 9 x 14 7 = Substitute lengths of the sides. 14 · x= 9 · 7 Find the cross product. Multiply. 14x = 63 63 14 14x 14 = Divide each side by 12 to isolate the variable. x = 4.5 HG is 4.5 centimeters.

  8. Check It Out: Example 1 Continued Find the unknown measures in the similar figures. D B A 27° 10 cm y 5.8 cm x 6 cm 116 cm 63° F E 5 cm C Step 2 Find y. Corresponding angles of similar triangles have equal angle measures. D corresponds to C y = 63

  9. Additional Example 2: Measurement Application The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle. Let x = the base of the inside triangle. 8 2 12 x Write a proportion using corresponding side lengths. = 8 · x = 2 · 12 Find the cross products. Multiply. 8x = 24 8x 8 24 8 = Divide each side by 8 to isolate the variable. x = 3 The base of the inside triangle is 3 inches.

  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. 12 cm 6 cm 3 cm ? Let w = the width of the right rectangle. 6 12 3 w Write a proportion using corresponding side lengths. = 6 ·w = 12 · 3 Find the cross products. Multiply. 6w = 36 36 6 6w 6 = Divide each side by 6 to isolate the variable. w = 6 The right rectangle is 6 cm wide.

  11. Additional Example 3: Estimating with Indirect Measurement City officials want to know the height of a traffic light. Estimate the height of the traffic light. 48.75 h 27.25 15 = Write a proportion. 25 15 Use compatible numbers to estimate. 50 h ≈ h ft 5 3 50 h Simplify. ≈ 27.25 ft Cross multiply. 5h ≈ 150 48.75 ft Divide each side by 5 to isolate the variable. h ≈ 30 The traffic light is about 30 feet tall.

  12. Check It Out: Example 3 The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle. h 30.25 5 14.75 = Write a proportion. Use compatible numbers to estimate. 5 15 h 30 ≈ h ft 5 ft 13 h 30 ≈ Simplify. Cross multiply. 1 • 30≈ 3• h 14.75 ft Divide each side by 3 to isolate the variable. 30≈ 3h 30.25 ft 10≈ h The outside triangle is about 10 feet tall.

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