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Using Similar Figures. 5-6. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 5-6. Using Similar Figures. JN. KO. Course 2. Warm Up. Solve each proportion. 24 x. 6 19. k 4. 75 25. x = 76. k = 12. 2. 1. =. =.

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  1. Using Similar Figures 5-6 Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 5-6 Using Similar Figures JN KO Course 2 Warm Up Solve each proportion. 24 x 6 19 k 4 75 25 x = 76 k = 12 2. 1. = = Triangles JNZ and KOA are similar. Identify the side that corresponds to the given side of the similar triangles. 3. A J Z O K N

  3. 5-6 Using Similar Figures Course 2 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

  4. 5-6 Using Similar Figures Course 2 Learn to use similar figures to find unknown lengths.

  5. 5-6 Using Similar Figures Course 2 Insert Lesson Title Here Vocabulary indirect measurement

  6. 5-6 Using Similar Figures Course 2 Indirect measurementis a method of using proportions to find an unknown length or distance in similar figures.

  7. 5-6 Using Similar Figures Course 2 Additional Example 1: Finding Unknown Lengths in Similar Figures Find the unknown length in 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. Multiply. 12w = 672 672 12 12w 12 = Divide each side by 12 to isolate the variable. w = 56 QR is 56 centimeters.

  8. 5-6 Using Similar Figures Course 2 Insert Lesson Title Here Check It Out: Example 1 Find the unknown length in similar figures. x Q R 10 cm B A 24 cm 12 cm D C T 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 to isolate the variable. = x = 20 QR is 20 centimeters.

  9. 5-6 Using Similar Figures Course 2 Insert Lesson Title Here 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. 5-6 Using Similar Figures Course 2 Insert Lesson Title Here 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. 5-6 Using Similar Figures Course 2 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. 5-6 Using Similar Figures Course 2 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.

  13. 5-6 Using Similar Figures Course 2 Insert Lesson Title Here Lesson Quiz: Part I Find the unknown length in each pair of similar figures. 1. x = 120 cm 2. t = 150 cm

  14. 5-6 Using Similar Figures Course 2 Insert Lesson Title Here Lesson Quiz: Part II Find the unknown length in each pair of 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. about 15 inches

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