Lesson 6 ~ Write and Solve Proportions Solve each proportion. 3 x 1. = 2. 4 20 5 25 8 a = 3. = 7 y 28 7 4. x 32 = 3 16 5. 6 12 = y 48 6. 3 5 = 15 b 7. 11 14 = x 28 8. 26 30 = x 15 9. 5 = 20 4 y Determine whether each pair of ratios forms a proportion. 5 40 10. and 9 44 18 12 11. and 21 14 7 35 12. and 12 60 Write a proportion for each phrase and solve it. 13. 3 feet in 1 second; 21 feet in x seconds 14. 7 pounds for $10.43; 10 pounds for a dollars 15. 25 miles in 30 minutes; y miles in 48 minutes
Lesson 7 ~ Problem-Solving With Proportions Solve each proportion. 7 x 1. = 2. 9 63 10 y = 25 20 Solve each problem using a proportion. The answers are listed at the bottom of the page out of order without units. Cross out each answer once you find it. 3. A bicyclist rides 18 miles in 2 hours. How far will the bicyclist ride at this speed in 5 hours? 4. Four posters cost $19.20. How many posters can you buy for $48.00? 5. You paid $28.00 for 8 gallons of gasoline. How much would you pay for 15 gallons of gasoline? 6. Tabitha walked 13.5 miles in three hours. At that speed, how many miles will she walk in seven hours? 7. Luis found a new text messaging plan which will charge him $2.00 for 80 messages. Using this plan, how much would he pay for 900 text messages in one month? 8. A truck driver travels 93 miles in 1 hour and 30 minutes. At this rate, how far will he travel in 4 hours? 9. Mark walked 21,129 feet in one hour. At that speed, about how many miles will he walk in two hours? 10. A 12 ounce soda costs $1.25 in the vending machine. At that rate, how much would a 32 ounce soda cost? Answers: 31.5 10 248 8 22.50 45 3.33 52.50
Lesson 8 ~ Similar and Congruent Figures For each pair of figures below, find the corresponding sides and corresponding angles to the ones identified. A 1. C 2. 60 6 ft S 3 ft A 60 30 3 ft 6 ft 5.2 ft R 30 5.2 ft U N D O 6 in 6 in 4 in 4 in 2 in G C 3 in T CA corresponds to AR corresponds to CR corresponds to C DO corresponds to D A OG corresponds to O R DG corresponds to G Are the triangles congruent or similar? Explain. Are the triangles congruent or similar? Explain. Determine the scale factor for each pair of similar figures. 3. 4. 40 in 30 in 8 cm 16 cm 5. 6. 15 mm 24 mm 15 yd 9 yd 7. 8. 5 m 15 m 4 m 12 m 12 ft 8 ft 21 ft 14 ft
Lesson 9 ~ Proportions and Similar Figures The shapes below are similar. Use proportions to solve for each variable. 5 in 1. 2. 2 in x in 15 in x in 18 in 4 in 9 in 3. 4. 28 ft 21 ft y ft 6 ft 44 m 11 m y m 8 m 5. 6. a ft 8 ft 108 ft 18 ft 18 in 24 in x in 4 in 7. Mike wanted to find the height of his pole barn. He measured the shadow from the pole barn on the ground to be 40 feet. He measured his own shadow on the ground to be 12 feet. Mike is 6 feet tall. Find the height of the pole barn. 8. Paula used a mirror to find the height of a tree in her backyard. She found her eye height to be 5.5 feet and her distance to the mirror to be 1.1 feet. The mirror was 12 feet from the tree. Find the height of the tree.
Lesson 10 ~ Special Ratios for Similar Figures Rectangle BIKE is similar to rectangle PLAY. 1. Find the scale factor. B I P L 2. Find the perimeter of each rectangle. 3. Find the ratio of the perimeters. 4. Find the area of each rectangle. 2 in E 6 in K 3 in Y 9 in A 5. Find the ratio of the areas. For each pair of similar figures: a. Find the scale factor. b. Find the ratio of the perimeters. c. Find the ratio of the areas. 6. 7. 1 in 14 ft 16 ft 6 in 8. 9. 12 m 20 m 75 cm 3 m 10. 11. 4 in 2 in 12 ft 15 ft 12. Use the similar figures to the right. a. If the smaller hexagon has a perimeter of 21 m, find the perimeter of the larger hexagon. 3 m 4 m b. If the larger hexagon has area 16 m 2, find the area of the smaller hexagon.
Lesson 11 ~ Scale Drawings A map has a scale 1 inches : 10 miles. Use the given map distance to find the actual distance. 1. 3 in 2. 7.5 in 3. 1 ft 4. 18 in A map has a scale 1 inch : 5 kilometers. Use the given actual distance to find the map distance. 5. 100 km 6. 45 km 7. 72 km 8. 9.5 km The cities of Lincoln City and Newport are 36 miles apart. Given the distance between the cities on each map, find the scale of each map. 9. 6 inches 10. 1 foot 11. A wall is 4 inches long in a scale drawing. The actual wall is 12 feet long. Find the scale of the drawing. 12. A sofa is 6 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the drawing. 13. A blue print of a house has a scale of 1 inch : 2 feet. a. Find the actual length of a wall that is 7 in on the blueprint. b. Find the actual height of a door that is 4 in on the blueprint. 14. You are building a model of a new roller coaster with a scale 1 : 51. The model is 4 ft tall. How tall is the actual roller coaster?