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

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

5-6 Using Similar Figures Problem of the Day Course 2 5-6 Using Similar Figures 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 minutes

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

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

5-6 Using Similar Figures 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.

Additional Example 1: Finding Unknown Lengths in Similar Figures Course 2 5-6 Using Similar Figures 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. 12 48 14 w = Substitute lengths of the sides. 12 · w = 48 · 14 Find the cross product. 12w = 672 Multiply. 12w 12 672 12 = Divide each side by 12 to isolate the variable. w = 56 QR is 56 centimeters.

Insert Lesson Title Here Course 2 5-6 Using Similar Figures Insert Lesson Title Here Try This: Example 1 Find the unknown length in similar figures. x 10 cm Q R A B 12 cm 24 cm D C S T 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 = 240 Multiply. 12x 12 240 12 = Divide each side by 12 to isolate the variable. x = 20 QR is 20 centimeters.

Additional Example 2: Measurement Application Course 2 5-6 Using Similar Figures Additional Example 2: Measurement Application A volleyball court is a rectangle that is similar in shape to an Olympic-sized swimming pool. Find the length of the pool. Let l = the length of the pool. 9 25 18 l Write a proportion using corresponding side widths. = 9 ·l = 18 · 25 Find the cross products. 9l = 450 Multiply. 9l 9 = 450 9 Divide each side by 9 to isolate the variable. l = 50 The pool is 50 meters long.

Insert Lesson Title Here Course 2 5-6 Using Similar Figures Insert Lesson Title Here Try This: 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. 6w = 36 Multiply. 6w 6 = 36 6 Divide each side by 6 to isolate the variable. w = 6 The right rectangle is 6 cm wide.

Additional Example 3: Using Indirect Measurement Course 2 5-6 Using Similar Figures Additional Example 3: Using Indirect Measurement City officials want to know the height of a traffic signal. The traffic light casts a shadow that is 45 ft long. A stop sign casts a shadow that is 30 ft long. If the stop sign is 15 ft high, what is the height of the traffic light? Let x = the height of the traffic light. 30 45 15 x = Write a proportion. 30 · x = 45 · 15 Find the cross product. 30 x = 675 Multiply. 30x 30 675 30 Divide each side by 30 to isolate the variable. = x = 22.5 The traffic light is 22.5 feet tall.

Insert Lesson Title Here Course 2 5-6 Using Similar Figures Insert Lesson Title Here Try This: Example 3 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. 8x = 24 Multiply. 8x 8 24 8 = Divide each side by 8 to isolate the variable. x = 3 The base of the inside triangle is 3 inches.

Insert Lesson Title Here Course 2 5-6 Using Similar Figures Insert Lesson Title Here Lesson Quiz Find the unknown length in each pair of similar figures. J A 3. These two rectangular cakes are similar in shape. How long is the larger cake? 144 cm 1. 96 cm x 80 cm C K 56 cm B L 84 cm 10 in. x = 120 cm 6 in. x 2. 9 in. 160 cm 120 cm t 72 cm 90 cm x = 15 inches t = 150 cm