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Understanding Ratios and Proportions in Scale Drawings

Learn how to calculate angles and lengths in similar triangles using the properties of similarity. Develop a solid understanding of ratios and proportions in scale drawings and scale models. Discover how to use scale factors to relate dimensions in drawings to the actual objects.

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Understanding Ratios and Proportions in Scale Drawings

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  1. Do Now The triangles below are similar. Use the properties of similarity to find the measure of angle A and the length of side EF.

  2. Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

  3. 1 87 1 87 A scale drawingis a proportional two-dimensional drawing of an object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. For example, if a drawing of a building has a scale factor of , this means that each dimension of the drawing is of the corresponding dimension of the actual building.

  4. A scale model is a proportional three- dimensional model of an object. A scale is the ratio between two sets of measurements. Scales can use the same units or different units.

  5. Caution! A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.

  6. Room Blueprint Length (in.)‏ 144 18 Width (in.)‏ 108 13.5 18 144 Example A: Identify the scale factor. blueprint length(model) room length(actual) 1 8 = =

  7. Model Aircraft Blueprint Length (in.)‏ 12 2 Wing span (in.)‏ 18 3 You Try: Identify the scale factor. 2 12 1 6 blueprint length(model) aircraft length(actual) = =

  8. Example B: On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? model actual 1.5in 60miles = Let d be the actual distance between the cities. 7.5in d miles 1.5in 60miles = 1.5d = 450 d = 300 miles

  9. You Try On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? model actual 1in 50km = Let d be the actual distance between the cities. 7in d km 1in 50km = d = 350 km

  10. Example C For solution refer to textbook page 173

  11. You Try A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 model actual 5 1 = 5 1 36 L 5 1 20.5 W = = 5L = 36 5w = 20.5 L= 7.2in w= 4.1in

  12. Statue of Liberty Model Height (in.)‏ 1,824 8 1 228 On a scale drawing, a kitchen wall is 6 inches long. The scale factor is . What is the length of the actual wall? 1 24 Lesson Quiz: Part I Identify the scale factor. 1. 2. 144 inches, or 12 feet

  13. Lesson Quiz: Part II 3. On a road map, the distance from Green Bay to Chicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km

  14. Lesson Quiz for Student Response Systems 1. Identify the scale factor. A. C. 10 B.D. 20 1 20 1 10

  15. Lesson Quiz for Student Response Systems 2. On a scale drawing, the height of a building is 60 inches. The scale factor is . What is the height of the actual building? A. 240 in., or 20 ft B. 300 in., or 25 ft C. 600 in., or 50 ft D. 900 in., or 75 ft 1 15

  16. Lesson Quiz for Student Response Systems 3. On a road map, the distance from Washington, DC to New York is 15 cm. What is the actual distance between the cities if the map scale is 3 cm = 50 mi? A. 150 mi B. 200 mi C. 250 mi D. 300 mi

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