The Pythagorean Theorem

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Presentation transcript:

The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 pages 587–590 Exercises 1. 10 2. 25 3. 17 4. 26 5. 2.5 6. 1 7. 4 8. 5 9. 12 10. 7.1 11. 7.5 12. 0.6 13. 1.2 m 14. about 15.5 ft 15. about 5.8 km 16. yes 17. no 18. no 19. yes 20. no 21. yes 22. yes 23. no 24. no 25. yes 26. 1.5 27. or 0.3 28. 3 29. 6 30. 2.6 31. 7.0 32. a. 6 5 ft b. 80.5 ft2 33. yes 34. no 4 15 11-2

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 41. 9.7 42. a. These lengths could be 2 legs or one leg and the hypotenuse. b. about 12.8 in. or 6 in. 43. a. 62 + 82 = 36 + 64 = 100 = 102 b. 5; 12; 7; 41 c. Answers may vary. Sample: 10, 24, 26 44. a. 6.9 ft b. 89.2 ft2 c. 981 watts 45. 12.8 ft 46. a. Answers may vary. Sample: 5, 20, 5 b. 5 units2 47. a. 13.4 ft b. 17.0 ft c. 10.6 ft d. No; the hypotenuse d must be longer than each leg. 48. An integer has 2 as a factor; the integer is even; if an integer is even, then it has 2 as a factor; true. 11-2

The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 54. 10 55. 4 3 56. 5 57. n2 + (n + 1)2 = (n + 2)2; 3, 4, 5 58. a. b. 74 59. a. a2 + 2ab + b2 b. c2 c. d. (a + b)2 = c2 + 4 ab ; a2 + 2ab + b2 = 2ab + c2; a2 + b2 = c2 e. This equation is the same as the Pythagorean Theorem. 49. A figure is a square; the figure is a rectangle; if a figure is a rectangle then the figure is a square; false. 50. You are in Brazil; you are south of the equator; if you are south of the equator you are in Brazil; false. 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. 52. 52 units2 53. 6 in. ab 2 1 2 11-2

The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 60. D 61. H 62. B 63. C 64. A 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 66. 4 3 67. 68. 5 2 69. 2b2 10b 70. 71. 72. 3 and 4 73. 8 and 9 74. –8 and –7 75. 11 and 12 76. rational 77. irrational 78. irrational 79. rational 2 2x2 2 6v v 4 – > – > 6 3 11-2

The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 80. 8x2 – 4x 81. 12a2 + 15a 82. 18t 3 – 6t 2 83. –10p4 + 26p3 84. 15b3 + 5b2 – 45b 85. –7v4 + 42v2 – 7v 11-2