2. Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Lesson 1 Contents Example 1Write a Ratio Example 2Extended Ratios in Triangles Example 3Solve Proportions by Using Cross Products Example 4Solve Problems Using Proportions

5. Example 1-1a The total number of students who participate in sports programs at Central High School is 520. The total number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth. Answer: The athlete-to-student ratio is 0.3. To find this ratio, divide the number of athletes by the total number of students. 0.3 can be written as

6. Example 1-1b The country with the longest school year is China with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.) Answer: 0.7

7. Example 1-2a Multiple- Choice Test Item In a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle. A 15 cm B 18 cm C 36 cm D 39 cm Read the Test Item You are asked to apply the ratio to the three sides of the triangle and the perimeter to find the shortest side. Solve the Test Item We can rewrite 5:12:13 as 5x:12x:13x and use those measures for the sides of the triangle. Write an equation to represent the perimeter of the triangle as the sum of the measures of its sides.

8. Example 1-2b Perimeter Combine like terms. Divide each side by 30.

9. Example 1-2c Use this value of x to find the measures of the sides of the triangle. Answer: A The shortest side is 15 centimeters. The answer is A. Check Add the lengths of the sides to make sure that the perimeter is 90.

10. Example 1-2d Multiple- Choice Test Item In a triangle, the ratio of the measures of three sides is 3:4:5, and the perimeter is 42 feet. Find the measure of the longest side of the triangle. A 10.5 ft B 14 ft C 17.5 ft D 37 ft Answer: C

11. Example 1-3a Original proportion Cross products Multiply. Answer: 27.3 Solve Divide each side by 6.

12. Example 1-3b Original proportion Cross products Simplify. Answer: –2 Add 30 to each side. Divide each side by 24. Solve

13. Example 1-3c Answer: 4.5 Answer: 9 Solve each proportion. a. b.

14. Example 1-4a A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model is made with a length of 16 inches. Find the width of the model. Because the scale model of the boxcar and the boxcar are in proportion, you can write a proportion to show the relationship between their measures. Since both ratios compare feet to inches, you need not convert all the lengths to the same unit of measure.

15. Example 1-4b Substitution Cross products Multiply. Divide each side by 40. Answer: The width of the model is 3.6 inches.

16. Example 1-4c Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container. Answer: 2.24 m

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