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

Course Using Similar Figures Warm Up Solve each proportion. 1. k4k4 = = 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

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 Using Similar Figures

Learn to use similar figures to find unknown lengths. Course Using Similar Figures

Vocabulary indirect measurement Insert Lesson Title Here Course Using Similar Figures

Course Using Similar Figures Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

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 = 14 w Substitute lengths of the sides. 12 · w = 48 · 14 Find the cross product. 12w = 672 Multiply. 12w 12 = w = 56 QR is 56 centimeters. Divide each side by 12 to isolate the variable. Course Using Similar Figures

Check It Out: Example 1 Insert Lesson Title Here Course 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 = 10 x Substitute lengths of the sides. 12 · x = 24 · 10 Find the cross product. 12x = 240Multiply. 12x 12 = x = 20 QR is 20 centimeters. Divide each side by 12 to isolate the variable. Find the unknown length in similar figures. x

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 Using Similar Figures Let x = the base of the inside triangle = 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

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 Using Similar Figures 3 cm 6 cm 12 cm Let w = the width of the right rectangle = 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. ?

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

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

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

Lesson Quiz: Part II Find the unknown length in each pair of similar figures. Insert Lesson Title Here Course 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