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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 24 x. 6 19. =. JN. KO. Warm Up. Solve each proportion. k 4. 75 25. k = 12. 2. 1. =. x = 76. Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. 3.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 24 x 6 19 = JN KO Warm Up Solve each proportion. k 4 75 25 k = 12 2. 1. = x = 76 Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. 3.

  3. California Standards NS1.3 Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. 4 7 N 21

  4. Vocabulary indirect measurement

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

  6. Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown length in the similar figures. AC QS AB QR = Write a proportion using corresponding sides. 14 w 12 48 = Substitute lengths of the sides. 12 · w = 48 · 14 Find the cross product. 12w = 672 Multiply. 672 12 12w 12 = Divide each side by 12. w = 56 QR is 56 centimeters.

  7. x 10 cm Q R B A 24 cm 12 cm D C T Check It Out! Example 1 Find the unknown length in the similar figures. S AC QS AB QR = Write a proportion using corresponding sides. 10 x 12 24 Substitute lengths of the sides. = Find the cross product. 12 · x = 24 · 10 12x = 240 Multiply. 240 12 12x 12 Divide each side by 12. = x = 20 QR is 20 centimeters.

  8. 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 product. Multiply. 8x = 24 8x 8 24 8 = Divide each side by 8. x = 3 The base of the inside triangle is 3 inches.

  9. 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 product. Multiply. 6w = 36 36 6 6w 6 = Divide each side by 6. w = 6 The right rectangle is 6 cm wide.

  10. 48.75 h 27.25 15 = 25 15 50 h ≈ 53 50 h ≈ 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. Write a proportion. Use compatible numbers to estimate. Simplify. 5h ≈ 150 Cross multiply. h ≈ 30 Divide each side by 5. The traffic light is about 30 feet high.

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

  12. Lesson Quiz Find the unknown length in each pair of similar figures. 1. 2. x = 120 cm t = 150 cm 3.The rectangles below are similar. The width of the smaller rectangle is 5.75 in. The width of a larger rectangle is 9.25 in. Estimate the length of the larger rectangle. about 15 inches

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