The Pythagorean Theorem ALGEBRA 1 LESSON 11 2

The Pythagorean Theorem ALGEBRA 1 LESSON 11 -2 pages 587– 590 Exercises 12. 0. 6 24. no 1. 10 13. 1. 2 m 25. yes 2. 25 14. about 15. 5 ft 26. 1. 5 3. 17 15. about 5. 8 km 27. 4 or 0. 3 4. 26 16. yes 28. 3 5. 2. 5 17. no 29. 6 6. 1 18. no 30. 2. 6 7. 4 19. yes 31. 7. 0 8. 5 20. no 9. 12 21. yes 32. a. 6 5 ft b. 80. 5 ft 2 10. 7. 1 22. yes 11. 7. 5 23. no 11 -2 15 33. yes 34. no

The Pythagorean Theorem ALGEBRA 1 LESSON 11 -2 35. yes 36. yes 37. 4. 2 cm 38. 1000 lb 39. 559. 9 40. 9. 0 44. a. 6. 9 ft b. 89. 2 ft 2 c. 981 watts 45. 12. 8 ft 46. a. Answers may vary. Sample: 5, 20, 5 b. 5 units 2 47. a. 13. 4 ft b. 17. 0 ft These lengths could be c. 10. 6 ft 2 legs or one leg and d. No; the hypotenuse d must the hypotenuse. be longer than each leg. about 12. 8 in. or 6 in. 48. An integer has 2 as a factor; 62 + 82 = 36 + 64 = 100 = 102 the integer is even; if an integer is even, then it has 2 as a factor; true. 5; 12; 7; 41 Answers may vary. Sample: 10, 24, 26 41. 9. 7 42. a. b. 43. a. b. c. 11 -2

The Pythagorean Theorem ALGEBRA 1 LESSON 11 -2 49. A figure is a square; the figure is a rectangle; if a figure is a rectangle then the figure is a square; false. 54. 10 50. You are in Brazil; you are south of the equator; if you are south of the equator you are in Brazil; false. 58. a. 51. An angle is a right angle; its measure is 90°; if the measure of an angle is 90°, then it is a right angle; true. 55. 4 3 56. 5 57. n 2 + (n + 1)2 = (n + 2)2; 3, 4, 5 b. 74 59. a. a 2 + 2 ab + b 2 b. c 2 c. ab 2 1 d. (a + b)2 = c 2 + 4 2 ab ; a 2 + 2 ab + b 2 = 2 ab + c 2; a 2 + b 2 = c 2 e. This equation is the same as the Pythagorean Theorem. 52. 52 units 2 53. 6 in. 11 -2

The Pythagorean Theorem ALGEBRA 1 LESSON 11 -2 60. D 69. 2 b 2 10 b 61. H 70. 63. C 2 2 x 2 71. 2 6 v v 4 64. A 72. 3 and 4 65. [2] It is a right triangle. Substitute 17, the longest side, for c and substitute the other lengths for a and b in the Pythagorean Theorem 82 + 152 172 –> 64 + 225 289 –> 289 = 289 [1] incorrect equation OR incorrect explanation 73. 8 and 9 62. B 66. 4 67. 3 75. 11 and 12 76. rational 77. irrational 78. irrational 6 3 68. 5 74. – 8 and – 7 79. rational 2 11 -2

The Pythagorean Theorem ALGEBRA 1 LESSON 11 -2 80. 8 x 2 – 4 x 81. 12 a 2 + 15 a 82. 18 t 3 – 6 t 2 83. – 10 p 4 + 26 p 3 84. 15 b 3 + 5 b 2 – 45 b 85. – 7 v 4 + 42 v 2 – 7 v 11 -2