Skills Practice Skills Practice for Lesson.1 Name Date Get Radical or (Be) 2! Radicals and the Pythagorean Theorem Vocabulary Write the term that best completes each statement. 1. An expression that includes a symbol such as A or A is called a(n). 2. A quantity that is enclosed by a radical symbol is called the.. The process of eliminating a radical from the denominator is called. 4. The states that a 2 b 2 c 2, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse of the triangle. Problem Set Simplify each radical expression completely. 1. 27 2. 50 9 9. 128 4. 112 5. 4 18 6. 6 72 7. a 2 b 5 8. x 4 y Chapter l Skills Practice 51
9. 9x 7 y 2 10. 24x y 5 Rationalize the denominator to simplify each radical expression completely. 11. 5 5 5 5 5 5 5 12. 5 6 1. 6 14. 15 5 15. 2 6 16. 2 2 8 17. 2ab b a 18. ab 5a 52 Chapter l Skills Practice
Name Date Use the Pythagorean Theorem to answer each question. 19. The interior of a small moving van has a height of 9 feet. A couch that is 8 feet long and 2.5 feet high is tipped on its end to fit in the van. Can the couch be set back on its feet while inside the moving van? a 2 b 2 c 2 (8) 2 (2.5) 2 c 2 64 6.25 c 2 70.25 c 2 70.25 c c 8.82 Because 8.82 feet is less than 9 feet, the couch can be set back on its feet while inside the moving van. 20. A firefighter has a 22-foot ladder. If he stands the bottom of the ladder 7 feet from the base of a building, will the ladder be long enough to reach a window 19 feet from the ground? 21. A baseball diamond is a square with sides of 90 feet. The first base player stands on first base and throws a ball to third base. To the nearest foot, what distance does the ball travel? Chapter l Skills Practice 5
22. A natural gas line is buried diagonally across a rectangular lot. The lot measures 240 feet by 162 feet. To the nearest foot, how much gas line is buried in the lot? 2. A guy wire is connected to the top of a 16-meter pole and to a point on the ground 8 meters from the bottom of the pole. To the nearest meter, what length is the guy wire? 24. Peter lives 10 miles directly north of a tower that broadcasts a wireless signal for his computer. If he drives directly east from his home, he can keep the wireless connection for 7 miles. About how many miles is the broadcasting range of the tower? 54 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson.2 Name Date The Pythagorean Theorem Disguised as the Distance Formula! The Distance Formula and Midpoint Formula Vocabulary Write each formula, explain how it is found, and explain why it is used. 1. the distance formula 2. the midpoint formula Chapter l Skills Practice 55
Problem Set Plot each pair of points and connect them with a line segment. Draw a right triangle with this line segment as the hypotenuse. Label the length of all three sides of the right triangle to the nearest tenth. 1. (0, 1) and (8, 5) 2. (2, 4) and (6, 8) y 10 8 6 4 2 8.9 4 10 8 6 4 2 0 2 8 2 4 x 6 8 10 4 6 8 10. ( 1, ) and (5, 1) 4. ( 6, 0) and (2, 4) 56 Chapter l Skills Practice
Name Date Use the distance formula to calculate the distance between each pair of points. Round decimal answers to the nearest thousandth. 5. (0, 1) and (8, 5) 6. (2, 4) and (6, 8) d (x 2 x 1 ) 2 ( y 2 y 1 ) 2 d (8 0) 2 (5 1) 2 d 64 16 d 80 d 4 5 8.944 7. ( 1, ) and (5, 1) 8. ( 6, 0) and (2, 4) 9. ( 6, 6) and ( 6, 12) 10. (, 7) and (0, 5) Use the given information to solve for y. 11. The distance between (6, 0) and (, y) is 10. d (x 2 x 1 ) 2 ( y 2 y 1 ) 2 10 ( 6) 2 ( y 0) 2 10 81 y 2 10 81 y 2 49 y 2 y 7 Chapter l Skills Practice 57
12. The distance between ( 5, 0) and (8, y) is 269. 1. The distance between ( 4, 0) and (6, y) is 116. 14. The distance between (8, 0) and (1, y) is 11. 58 Chapter l Skills Practice
Name Date Use the midpoint formula to calculate the midpoint between each pair of points. 15. (0, 1) and (8, 5) ( x x 1 2, y y 1 2 2 2 ) ( 0 8 2, 1 5 2 ) ( 8 2, 6 2 ) (4, ) 16. (2, 4) and (6, 8) 17. ( 1, ) and (5, 1) 18. ( 6, 0) and (2, 4) 19. ( 12, 16) and ( 4, 9) 20. ( 9, 8) and (0, 10) Use the given information to solve for x. 21. The point (, 0) is the midpoint of a line segment with endpoints (7, 4) and (x, 4). ( x x 1 2, y y 1 2 2 2 ) ( 7 x 4, ( 4) 2 2 ) ( 7 x 2, 0 2 ) ( 7 x 2, 0 ) (, 0) 7 x 2 7 x 6 x 1 22. The point ( 6, 2) is the midpoint of a line segment with endpoints (1, 1) and (x, 5). Chapter l Skills Practice 59
2. The point (5, 7) is the midpoint of a line segment with endpoints (0, 2) and (x, 16). 24. The point ( 8, 4) is the midpoint of a line segment with endpoints ( 1, 2) and (x, 10). 60 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson. Name Date Drafting Equipment Properties of 45º 45º 90º Triangles Vocabulary Explain how to find each of the following. 1. the leg length of a 45º 45º 90º triangle when you know the length of the other leg 2. the leg length of a 45º 45º 90º triangle when you know the length of the hypotenuse. the hypotenuse of a 45º 45º 90º triangle when you know the length of a leg 4. the area of a 45º 45º 90º triangle Chapter l Skills Practice 61
Problem Set Determine the unknown side length of each triangle. 1. 2. m c 4 2 cm c m c ( 2 ) 2 m 4 2 cm. 45 4. 45 18 inches a 11 feet a 45 45 Use the 45º 45º 90º Triangle Theorem to calculate the indicated length. 5. What is the leg length of an isosceles right triangle with a hypotenuse of 6 inches? Let a leg length and c hypotenuse length. a 2 c a 2 6 a 6 6 2 2 2 6 2 2 2 2 The leg length is 2 inches. 62 Chapter l Skills Practice
Name Date 6. What is the leg length of an isosceles right triangle with a hypotenuse of 28 centimeters? 7. What is the length of the hypotenuse of an isosceles right triangle with a leg length of 7 feet? 8. What is the length of the hypotenuse of an isosceles right triangle with a leg length of meters? 9. The side length of a square is 4.5 feet. What is the length of the diagonal? Chapter l Skills Practice 6
10. The side length of a square is 2 2 feet. What is the length of the diagonal? 11. The length of the diagonal of a square is 2 feet. What is the length of each side? 12. The length of the diagonal of a square is 80 millimeters. What is the length of each side? 64 Chapter l Skills Practice
Name Date Calculate the area of each triangle. 1. 14. 45 45 5 feet 45 A 1 2 bh A 1 2 (5)(5) A 1 2 (25) A 12.5 square feet 12.4 meters 15. 45 16. 45 4.8 inches 15 feet 45 Chapter l Skills Practice 65
Calculate the area of each square. 17. 18. 6.2 meters 12 inches A s 2 A (6.2) 2 A 8.44 square meters 19. 20. 5 cm 17 mm 66 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson.4 Name Date Finishing Concrete Properties of 0º 60º 90º Triangles Vocabulary Answer each question in your own words. 1. How are the side lengths of a 0º 60º 90º triangle related? 2. How is a 0º 60º 90º triangle used to find the altitude of an equilateral triangle? Problem Set Use the Pythagorean Theorem to calculate the missing side length of each triangle. Leave radicals in simplest form. 1. 2. 8 c 8 a 8, b 8 a 2 b 2 c 2 (8) 2 (8 ) 2 c 2 a 14 7 cm 64 64() c 2 256 c 2 16 c c 16 units Chapter l Skills Practice 67
. A right triangle has a hypotenuse length of 40 units and one leg length of 20 units. Find the length of the other leg. 4. A right triangle has a hypotenuse length of 12 units and one leg length of 6 units. Find the length of the other leg. 68 Chapter l Skills Practice
Name Date Use the 0º 60º 90º Triangle Theorem to calculate the missing side lengths in each triangle. Leave radicals in simplest form. 5. 6. b 0 4 cm 0 a 18 m b a shorter leg: 2a 4 a 2 cm longer leg: b a 2 cm 7. 8. a c a c 0 0 6 ft 2 in Chapter l Skills Practice 69
9. A 0º 60º 90º triangle has a shorter leg that measures 0 inches. Find the length of the longer leg and the length of the hypotenuse. 10. A 0º 60º 90º triangle has a shorter leg that measures 14 inches. Find the length of the longer leg and the length of the hypotenuse. 70 Chapter l Skills Practice
Name Date Use the 0º 60º 90º Triangle Theorem to calculate the missing measurement of each equilateral triangle. Leave radicals in simplest form. 11. An equilateral triangle has a side length of 100 inches. What is the measurement of the altitude? The altitude divides the equilateral triangle into two 0º 60º 90º triangles. The side length is the hypotenuse and the altitude is the longer leg. Find the shorter leg first. hypotenuse: c 2a 100 2a a 50 longer leg: b a 50 inches The measurement of the altitude is 50 inches. 12. An equilateral triangle has a side length of 22 inches. What is the measurement of the altitude? Chapter l Skills Practice 71
1. The altitude of an equilateral triangle has a measurement of 4 feet. What is the side length? 14. The altitude of an equilateral triangle has a measurement of 42 millimeters. What is the side length? 72 Chapter l Skills Practice
Name Date Calculate the area of each triangle. 15. 16. 8 in 7 ft 0 0 height 4 inches base 4 inches area 1 2 bh 1 2 (4 )(4) 8 square inches 17. 18. cm 70 mm Chapter l Skills Practice 7
Calculate the surface area and volume of each triangular prism. Round decimals to the nearest tenth. 19. 2 in 0 12 in Triangular base: a 2, b 2, c 4 B 1 2 (2)(2 ) 2 P 2 2 4 6 2 S 2(2 ) (6 2 )(12) 4 72 24 72 28 120.5 square inches V 1 2 (2)(2 )(12) 24 41.6 cubic inches 20. 6 cm 20 cm 74 Chapter l Skills Practice
Name Date 21. 18 ft 15 ft 0 0 22. 2 m 9 m Chapter l Skills Practice 75
76 Chapter l Skills Practice