7-4 Similar Figures Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

7-4 Similar Figures Warm Up Fill in the missing value. 1. c = 2 qt in. = yd 3. 3 tons = lb 4. min = 2,760 s 8 5 6,000 46

7-4 Similar Figures Problem of the Day How many 8 in. by 10 in. rectangular tiles would be needed to cover a 16 ft by 20 ft floor? 576

7-4 Similar Figures Learn to use proportions to find missing measures in similar figures.

7-4 Similar Figures Vocabulary corresponding sides corresponding angles similar

7-4 Similar Figures Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

7-4 Similar Figures Two figures are similar if the measures of the corresponding angles are equal. the ratios of the lengths of the corresponding sides t are proportional. Similar Figures Similar figures have the same shape but not necessarily the same size.

7-4 Similar Figures Additional Example 1: Finding Missing Measures in Similar Figures 111 y ___ ____ = Write a proportion using corresponding side lengths. The cross products are equal = 100 y The two triangles are similar. Find the missing length y and the measure of D.

7-4 Similar Figures Additional Example 1 Continued y is multiplied by ,200 = 100y 22, ______ 100y 100 ____ = Divide both sides by 100 to undo the multiplication. 222 mm = y Angle D is congruent to angle C, and m C = 70°. m D = 70° The two triangles are similar. Find the missing length y and the measure of D.

7-4 Similar Figures Check It Out: Example 1 52 y ___ ____ = Write a proportion using corresponding side lengths. The cross products are equal = 50 y A B 60 m120 m 50 m 100 m y 52 m 65° 45° The two triangles are similar. Find the missing length y and the measure of B.

7-4 Similar Figures Check It Out: Example 1 Continued y is multiplied by 50.5,200 = 50y 5, _____ 50y 50 ___ = Divide both sides by 50 to undo the multiplication. 104 m = y Angle B is congruent to angle A, and m A = 65°. m B = 65° The two triangles are similar. Find the missing length y and the measure of B.

7-4 Similar Figures This reduction is similar to a picture that Katie painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting? 1 Understand the Problem The answer will be the width of the actual painting. List the important information: The actual painting and the reduction above are t similar. The reduced painting is 2 cm tall and 3 cm wide. The actual painting is 54 cm tall. Additional Example 2: Problem Solving Application

7-4 Similar Figures Additional Example 2 Continued Draw a diagram to represent the situation. Use the corresponding sides to write a proportion. 2 Make a Plan Reduced Actual w

7-4 Similar Figures Additional Example 2 Continued Solve = 2 w 162 = 2w ____ 2w 2 ___ = 81 = w The width of the actual painting is 81 cm. Write a proportion. The cross products are equal. w is multiplied by 2. Divide both sides by 2 to undo the multiplication. 3 cm w cm 2 cm 54 cm _____ =

7-4 Similar Figures Additional Example 2 Continued Look Back4 Estimate to check your answer. The ratio of the heights is about 2:54 or 1:27. The ratio of the widths is about 3:81, or 1:27. Since these ratios are equal, 81 cm is a reasonable answer.

7-4 Similar Figures Check It Out: Example 2 This reduction is similar to a picture that Marty designed. The height of the actual picture is 39 inches. What is the width of the actual picture? 1 Understand the Problem The answer will be the width of the actual painting. List the important information: The actual painting and the reduction above are t similar. The reduced painting is 3 in. tall and 4 in. wide. The actual painting is 39 in. tall. 4 in. 3 in.

7-4 Similar Figures Check It Out: Example 2 Continued Draw a diagram to represent the situation. Use the corresponding sides to write a proportion. 2 Make a Plan Reduced Actual w

7-4 Similar Figures Check It Out: Example 2 Continued Solve 3 4 in w in ____ 3 in 39 in _____ = 39 4 = 3 w 156 = 3w ____ 3w 3 ___ = 52 = w The width of the actual painting is 52 inches. Write a proportion. The cross products are equal. w is multiplied by 3. Divide both sides by 3 to undo the multiplication.

7-4 Similar Figures Check It Out: Example 2 Continued Look Back4 Estimate to check your answer. The ratio of the heights is about 4:40, or 1:10. The ratio of the widths is about 5:50, or 1:10. Since these ratios are the same, 52 inches is a reasonable answer.

7-4 Similar Figures Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

7-4 Similar Figures Lesson Quiz These two triangles are similar. 1. Find the missing length x. 2. Find the measure of J. 3. Find the missing length y. 4. Find the measure of P. 5. Susan is making a wood deck from plans for an 8 ft by 10 ft deck. However, she is going to increase its size proportionally. If the length is to be 15 ft, what will the width be? 36.9° 30 in. 4 in. 90° 12 ft

7-4 Similar Figures 1. These two triangles are similar. Identify the missing length x. A. 3 cm B. 4 cm C. 5 cm D. 6 cm Lesson Quiz for Student Response Systems

7-4 Similar Figures 2. These two triangles are similar. Identify the measure R. A. 30 B. 50 C. 80 D. 90 Lesson Quiz for Student Response Systems

7-4 Similar Figures 3. These two triangles are similar. Identify the missing length y. A. 27 in. B. 21 in. C. 9 in. D. 8 in. Lesson Quiz for Student Response Systems

7-4 Similar Figures 4. A carpenter is making a rectangular table top of dimensions 9 ft by 12 ft. However, he is going to increase its size proportionally. If the width is to be 15 ft, what will the length be? A. 24 ft B. 20 ft C. 18 ft D. 12 ft Lesson Quiz for Student Response Systems