MA.7.A.1.3: Solve problems involving similar figures. Scale Factor Scale Factor- the ratio to two corresponding sides of two geometric figures. Corresponding sides change by the same scale factor. What does this mean? It means that all the sides of the small figure are multiplied by the same number to obtain the lengths of the corresponding sides of the large figure. The scale factor of figure A to B is: 3 3 * 3 = 9; 5 * 3 = 15 The scale factor of figure B to A is: 1/3 9 * 1/3 = 3; 15 * 1/3 = 5 How does the scale factor going from the large figure to the small figure compare to the scale factor of the small figure to the large figure? It is the reciprocal of the scale factor from the small to the large. Example: 20 Scale factor: 15 newfigure 10 1 = = orginalfigure 20 2 10 7.5 newfigure 7 .5 1 = = orginalfigure 15 2 Proportion- an equation stating that two ratios or rates are equivalent. Example: A picture that was 5 inches long and 3 inches wide was enlarged so that the new picture is 1 foot long. What is the width of the new picture? 12inches 5inches length (in ) = = = Cross multiply 5x = 12 • 3 x 3inches width (in ) 5x = 36 x = 7.2 inches I changed the 1 foot to 12 inches so the same unit of measurement was used throughout. **Hint: Notice Example: Find the length of the missing side. 3 ft. 15 ft. 8 ft. x 3 ft 15 ft 8 ft x Set up the proportion: Cross multiply: Divide by 3: Solve for x: 3•x = 8•15 3x = 120 x = 120 ÷ 3 x = 40 MA.7.A.1.3 Practice Problems Find the value of x in each pair of figures: 2. 5ft Directions: Using the diagrams below answer questions 3 and 4. 3) What is the scale factor from triangle CAT to triangle DOG? 4) How many times bigger is the area of triangle CAT than the area of triangle DOG? (Hint: Find the area of each and then compare!!!) 5) What is the scale factor from triangle UVW to triangle XYZ? What is the scale factor from triangle XYZ to triangle UVW? What is the length of XZ? What is the length of YZ? 6) The sketch shows two similar polygons. a. What is the length of side BC? b. What is the length of side RU? c. What is the length of side CD? 7. Solve for x and y. 28 yd. 5 yd. 25 yd. y x 7 yd. 8. State whether the following statements are true or false: a. All squares are similar. b. All rectangles are similar. 9. 10. Judy lies on the ground 45 feet from her tent. Both the top of the tent and the top of a tall cliff are in her line of sight. Her tent is 10 feet tall. About how high is the cliff?
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