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Proportions in Similar Figures

Learn how to use proportions to find missing measures in similar figures. Explore corresponding sides, angles, and vocabulary. Solve real-world application problems.

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Proportions in Similar Figures

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  1. 7-4 Similar Figures Course 1 Warm Up Problem of the Day Lesson Presentation

  2. Warm Up Fill in the missing value. 1. c = 2 qt 2. 180 in. = yd 3. 3 tons = lb 4. min = 2,760 s 8 5 6,000 46

  3. 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

  4. Learn to use proportions to find missing measures in similar figures.

  5. Vocabulary corresponding sides corresponding angles similar

  6. Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

  7. Similar figures have the same shape but not necessarily the same size.

  8. The two triangles are similar. Find the missing length y and the measure of D. 111 100 ___ ____ y 200 Additional Example 1: Finding Missing Measures in Similar Figures Write a proportion using corresponding side lengths. = 200 • 111= 100 •y The cross products are equal.

  9. The two triangles are similar. Find the missing length y and the measure of D. 22,200 100y ______ ____ 100 100 Additional Example 1 Continued 22,200= 100y y is multiplied by 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°

  10. 52 50 ___ ____ y 100 Check It Out: Example 1 The two triangles are similar. Find the missing length y and the measure of B. B A 60 m 120 m 65° 50 m 100 m 52 m 45° y Write a proportion using corresponding side lengths. = 100 • 52= 50 •y The cross products are equal.

  11. 5,200 50y _____ ___ 50 50 Check It Out: Example 1 Continued The two triangles are similar. Find the missing length y and the measure of B. 5,200= 50y y is multiplied by 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°

  12. 1 Understand the Problem Additional Example 2: Problem Solving Application 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? • 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.

  13. Make a Plan 2 Additional Example 2 Continued Draw a diagram to represent the situation. Use the corresponding sides to write a proportion. Actual Reduced 2 54 3 w

  14. 3 Solve 3 cm = w cm 2 cm 162 2w ____ ___ _____ 2 54 cm 2 Additional Example 2 Continued Write a proportion. 54 • 3= 2 •w The cross products are equal. w is multiplied by 2. 162= 2w Divide both sides by 2 to undo the multiplication. = 81= w The width of the actual painting is 81 cm.

  15. Look Back 4 Additional Example 2 Continued Estimate to check your answer. The ratio of the heights is about 2:50 or 1:25. The ratio of the widths is about 3:90, or 1:30. Since these ratios are close to each other, 81 cm is a reasonable answer.

  16. 1 Understand the Problem Check It Out: Example 2 4 in. 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? 3 in. • 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.

  17. Make a Plan 2 Check It Out: Example 2 Continued Draw a diagram to represent the situation. Use the corresponding sides to write a proportion. Actual Reduced 3 39 4 w

  18. 3 Solve 156 4 in 3 in 3w ____ _____ ___ ____ 3 3 w in 39 in Check It Out: Example 2 Continued = Write a proportion. 39 • 4= 3 •w The cross products are equal. w is multiplied by 3. 156= 3w Divide both sides by 3 to undo the multiplication. = 52= w The width of the actual painting is 52 inches.

  19. Look Back 4 Check It Out: Example 2 Continued 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.

  20. 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? 30 in. 36.9° 4 in. 90° 12 ft

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