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Our Learning Goal for Chapter 8

Our Learning Goal for Chapter 8.

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Our Learning Goal for Chapter 8

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  1. Our Learning Goal for Chapter 8 Students will understand ratios, proportions, and percents by being able to write ratios, find unit rates, solve proportions, identify similar figures, find unknown measures, make scale drawings, understand relationships, and solve problems including those involving discounts, tips, sales tax, and simple interest.

  2. Our Learning Goal Assignments • Learn to write ratios and rates and to find unit rates (8-1) • Learn to write and solve proportions (8-2) • Learn to use proportions to make conversions within the customary system (8-3) • Learn to use ratios to identify similar figures (8-4) • Learn to use proportions and similar figures to find unknown measures (8-5) • Learn to read and use map scale and scale drawings (8-6) • Learn to write percents as decimals and as fractions (8-7) • Learn to write decimals and fractions as percents (8-8) • Learn to find the missing value in a percent problem (8-9) • Learn to solve percent problems that involve discounts, tips, and sales tax (8-10)

  3. 8-4 Similar Figures Course 1 Warm Up Problem of the Day Lesson Presentation

  4. 8-4 Similar Figures Course 1 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 45

  5. 8-4 Similar Figures Course 1 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

  6. 8-4 Similar Figures Course 1 Today’s Learning Goal Assignment Learn to use ratios to identify similar figures.

  7. 8-4 Similar Figures Course 1 Insert Lesson Title Here Vocabulary similar corresponding sides corresponding angles

  8. 8-4 Similar Figures Course 1 Two or more figures are similar if they have exactly the same shape. Similar figures may be different sizes. • Similar figures have corresponding sides and corresponding angles. • Corresponding sides have lengths that are proportional. • Corresponding angles are congruent.

  9. 8-4 Similar Figures 9 cm W Z 3 cm A D 2 cm 2 cm 6 cm 6 cm B C 3 cm Y X 9 cm AB corresponds to WX. Acorresponds to W. B corresponds to X. BCcorresponds to XY. CDcorresponds to YZ. Ccorresponds to Y. ADcorresponds to WZ. Dcorresponds to Z. Course 1 Corresponding sides: Corresponding angles:

  10. 8-4 Similar Figures 9 cm W Z 3 cm A D 2 cm 2 cm 6 cm 6 cm B C 3 cm Y X 9 cm In the rectangles above, one proportion is = , or = . AB WX AD WZ 2 6 3 9 Course 1 If you cannot use corresponding side lengths to write a proportion, or if corresponding angles are not congruent, then the figures are not similar.

  11. 8-4 Similar Figures The two triangles are similar. Find the missing length y and the measure of D. 111 100 ___ ____ y 200 Course 1 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.

  12. 8-4 Similar Figures The two triangles are similar. Find the missing length y and the measure of D. 100y 22,200 ____ ______ 100 100 Course 1 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°

  13. 8-4 Similar Figures The two triangles are similar. Find the missing length y and the measure of B. 52 50 ____ ___ y 100 Course 1 Try This: Example 1 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.

  14. 8-4 Similar Figures The two triangles are similar. Find the missing length y and the measure of B. 50y 5,200 ___ _____ 50 50 Course 1 Try This: Example 1 Continued 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°

  15. 8-4 Similar Figures 1 Understand the Problem Course 1 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 similar. • The reduced painting is 2 cm tall and 3 cm wide. • The actual painting is 54 cm tall.

  16. 8-4 Similar Figures Make a Plan 2 Course 1 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

  17. 8-4 Similar Figures 3 Solve 3 cm = w cm 2 cm 162 2w _____ ___ ____ 54 cm 2 2 Course 1 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.

  18. 8-4 Similar Figures Look Back 4 Course 1 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.

  19. 8-4 Similar Figures 1 Understand the Problem Course 1 Try This: Example 2 This reduction is similar to a picture that Marty painted. The height of the actual painting is 39 inches. What is the width of the actual painting? 4 in. 3 in. • The answer will be the width of the actual painting. • List the important information: • The actual painting and the reduction above are similar. • The reduced painting is 3 in. tall and 4 in. wide. • The actual painting is 39 in. tall.

  20. 8-4 Similar Figures Make a Plan 2 Course 1 Try This: Example 2 Continued Draw a diagram to represent the situation. Use the corresponding sides to write a proportion. Actual Reduced 3 39 4 w

  21. 8-4 Similar Figures 3 Solve 3 in 4 in 3w 156 ____ ____ _____ ___ w in 39 in 3 3 Course 1 Try This: 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.

  22. 8-4 Similar Figures Look Back 4 Course 1 Try This: 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.

  23. 8-4 Similar Figures Course 1 Insert Lesson Title Here 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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