1. 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 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
or 0.3
28. 3
29. 6
32. a ft
b ft2
33. yes
34. no 4 15
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2. The Pythagorean Theorem
ALGEBRA 1 LESSON 11-2
35. yes
36. yes cm lb
42. a. These lengths could be
2 legs or one leg and
the hypotenuse.
b. about 12.8 in. or 6 in.
43. a = = 100 = 102
b. 5; 12; 7; 41
c. Answers may vary. Sample: 10, 24, 26
44. a. 6.9 ft
b ft2
c. 981 watts ft
46. a. Answers may vary.
Sample: 5, , 5
b. 5 units2
47. a ft
b ft
c 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.
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3. The Pythagorean Theorem
ALGEBRA 1 LESSON 11-2
54. 10
56. 5
57. n2 + (n + 1)2 = (n + 2)2; 3, 4, 5
58. a. b
59. a. a2 + 2ab + b2
b. c2 c.
d. (a + b)2 = c 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.
units2
53. 6 in. ab 2 1 2
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4. 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
= 289
[1] incorrect equation OR incorrect explanation
67.
69. 2b b
70.
71.
72. 3 and 4
73. 8 and 9
74. –8 and –7
and 12
76. rational
77. irrational
78. irrational
79. rational 2
2x2
2 6v
v 4 –
> –
> 6 3
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5. 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