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# 6.2 use proportions to solve geometry problems

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• 1. 6.2 Use Proportions to Solve Geometry Problems 6.2 Bell Thinger Solve each proportion. 6 1. 3 = 8 x+1 ANSWER 15 8 = x+1 3 6 ANSWER 15 2. 3. 3 = 8 6 x+1 ANSWER 15 4. The area of a rectangle is 750 square meters. The ratio of the width to the length is 5 : 6. Find the width and the length. ANSWER width: 25 m; length: 30 m
• 2. 6.2
• 3. Example 1 6.2 In the diagram, MN = NP RS ST Write four true proportions. SOLUTION Because MN = NP , then 8 = 4 RS ST x 10 By the Reciprocal Property, the reciprocals are 10 equal, so x = 4 8 By Property 3, you can interchange the means, so 10 8 = x 4 By Property 4, you can add the denominators to the numerators, so 8 + 10 4 + x , or 18 = = 10 x 10 4+x . x
• 4. Example 2 6.2 ALGEBRA In the diagram, BD = BE . DA EC Find BA and BD. SOLUTION BD DA BD + DA DA x 3 6x = = = = BE EC BE + EC EC 18 + 6 6 3(18 + 6) x = 12 Given Property of Proportions (Property 4) Substitution Property of Equality Cross Products Property Solve for x. So, BA = 12 and BD = 12 – 3 = 9.
• 5. 6.2
• 6. Example 3 6.2 Blueprints The blueprint shows a scale drawing of a cell phone. The length of the antenna on the blueprint is 5 centimeters. The actual length of the antenna is 2 centimeters. What is the scale of the blueprint? SOLUTION To find the scale, write the ratio of a length in the drawing to an actual length, then rewrite the ratio so that the denominator is 1. length on blueprint 5÷2 5 cm 2.5 = 2 cm = 2 ÷ 2 = 1 length of antenna The scale of the blueprint is 2.5 cm : 1 cm.
• 7. Guided Practice 6.2 In the diagram, MN = NP RS ST 1. Find the value of x. ANSWER 5 2. Suppose the length of the antenna on the blueprint is 10 centimeters (actual length 2 cm). Find the new scale of the blueprint. ANSWER 5 cm 1 cm
• 8. Example 4 6.2 Maps The scale of the map at the right is 1 inch : 26 miles. Find the actual distance from Pocahontas to Algona. SOLUTION Use a ruler. The distance from Pocahontas to Algona on the map is about 1.25 inches. Let x be the actual distance in miles. distance on map 1.25 in. 1 in. = x mi actual distance 26 mi x = 1.25 (26) Cross Products Property Simplify. x = 32.5 The actual distance from Pocahontas to Algona is about 32.5 miles.
• 9. Example 5 6.2 Scale Model You buy a 3-D scale model of the Reunion Tower in Dallas, TX. The actual building is 560 feet tall. Your model is 10 inches tall, and the diameter of the dome on your scale model is about 2.1 inches. a. What is the diameter of the actual dome? b. About how many times as tall as your model is the actual building?
• 10. Example 5 6.2 SOLUTION a. 10 in. = 2.1 in. 560 ft x ft 10 x = 1176 x = 117.6 measurement on model measurement on actual building Cross Products Property Solve for x. The diameter of the actual dome is about 118 feet. b. To simplify a ratio with unlike units, multiply by a conversion factor. 560 ft 10 in. = 560 ft 10 in. 12 in. = 672 1 ft The actual building is 672 times as tall as the model.
• 11. Guided Practice 6.2 4. Two cities are 96 miles from each other. The cities are 4 inches apart on a map. Find the scale of the map. ANSWER 1 in : 24 mi
• 12. Exit Slip 6.2 1. In the diagram, RS = ST . Write four true XY YZ proportions. ANSWER 45 = 30 30 = x 24 45 Sample answer : = x ; 45 x ; 24 ; 24 30 45 + 30 = 24 + x x 30
• 13. Exit Slip 6.2 PS 2. In the diagram, MR = . find MN and MR. SN RN ANSWER 48; 30
• 14. Exit Slip 6.2 3. On a map, a street is 2 inches long. The actual length is 1 mile. Find the scale. ANSWER 4. 1 in. : 0.5 mi A map’s scale is 1 cm : 20 km. If two towns are 8.2 centimeters apart on the map, what is the actual distance between them? ANSWER 164 km
• 15. Exit Slip 6.2 5. Solve ANSWER 6. 1 = 3 s+8 36 4 Find the geometric mean of 42 and 12. ANSWER 6 14
• 16. Exit Slip 6.2 7. The extended ratio of the angles of a triangle is 5: 12: 13. Find the angle measures of the triangle. ANSWER 8. 30 , 72°, 78° The area of a rectangle is 720 square inches. If the ratio of the length to the width is 5 : 4, find the perimeter of the rectangle. ANSWER 108 in.
• 17. 6.2 Homework Pg 383-386 #8, 12, 15, 16, 22