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

2. Course 2 5-6 Using Similar Figures Warm Up Solve each proportion. 1. k4k4 = 75 25 2.2. 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 JNKO 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 5-6 Using Similar Figures

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

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

6. Course 2 5-6 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 5-6 Using Similar Figures

8. Check It Out: Example 1 Insert Lesson Title Here Course 2 5-6 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 = 240Multiply. 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 5-6 Using Similar Figures Let x = the base of the inside triangle. 8282 = 12 x 8 · x = 2 · 12 8x = 24 8x88x8 = 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 5-6 Using Similar Figures 3 cm 6 cm 12 cm Let w = the width of the right rectangle. 6 12 = 3w3w 6 ·w = 12 · 3 6w = 36 6w66w6 = 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 5-6 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. 5353 ≈ 50 h Simplify. 5h ≈ 150 The traffic light is about 30 feet tall. 27.25 ft 48.75 ft h ft 25 15 ≈ 50 h Cross multiply. h ≈ 30 Divide each side by 5 to isolate the variable.

12. Check It Out: Example 3 Course 2 5-6 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. 1313 ≈ 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 Divide each side by 3 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 5-6 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 5-6 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. about 15 inches