6.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Proportions to Solve Geometry Problems

6.2 Warm-Up ANSWER 15 Solve each proportion = x + 1x = x + 1x ANSWER 15 ANSWER = x + 1x + 1 8

6.2 Warm-Up ANSWER width: 25 m; length: 30 m 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.

6.2 Example 1 SOLUTION NP ST MN RS = Because 4 x = 8 10, then In the diagram, NP ST MN RS = Write four true proportions. By the Reciprocal Property, the reciprocals are equal, so x 4 = 10 8

6.2 Example 1 By Property 3, you can interchange the means, so = 10 x 8 4 By Property 4, you can add the denominators to the numerators, so x x x =, or =.

6.2 Example 2 Given Property of Proportions (Property 4 ) Substitution Property of Equality Cross Products Property Solve for x. BE EC BD DA = SOLUTION = x 3 x 12 = 6x6x3(18 + 6) = So, BA = 12 and BD = 12 – 3 = 9. ALGEBRA In the diagram,. BE EC BD DA = Find BA and BD. = BE + EC EC BD + DA DA

6.2 Example 3 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. The scale of the blueprint is 2.5 cm : 1 cm. = 5 cm 2 cm = = 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? Blueprints length on blueprint length of antenna

6.2 Guided Practice 1. In Example 1, find the value of x. ANSWER 5 2. In Example 2,. Find AC. BE BC DE AC = ANSWER WHAT IF? In Example 3, suppose the length of the antenna on the blueprint is 10 centimeters. Find the new scale of the blueprint. 5 cm 1 cm ANSWER

6.2 Example 4 SOLUTION Maps The scale of the map at the right is 1 inch : 26 miles. Find the actual distance from Pocahontas to Algona. 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.

6.2 Example 4 Cross Products Property Simplify. = 1.25 (26) x x = 32.5 The actual distance from Pocahontas to Algona is about 32.5 miles in. x mi 26 mi 1 in. = distance on map actual distance

6.2 Example 5 What is the diameter of the actual dome? a. b. About how many times as tall as your model is the actual building? 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.

6.2 Example 5 Cross Products Property measurement on model measurement on actual building = x x = SOLUTION 10 in. 560 ft x ft 2.1 in. = a. 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. = 672 The actual building is 672 times as tall as the model. 1 ft 12 in. 560 ft 10 in. =

6.2 Guided Practice 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 5. WHAT IF? Your friend has a model of the Reunion Tower that is 14 inches tall. What is the diameter of the dome on your friend’s model? ANSWER About 2.95 in.

6.2 Lesson Quiz 1. In the diagram,. Write four true proportions. RS XY ST YZ = ANSWER Sample answer : = 24 x = x = 30 x = 24 + x x ; ; ;

6.2 Lesson Quiz 2. In the diagram,. find MN and MR. MR RN PS SN = ANSWER 48; 30

6.2 Lesson Quiz 3. On a map, a street is 2 inches long. The actual length is 1 mile. Find the scale. ANSWER 1 in. : 0.5 mi 4. 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