1. Pythagorean Theorem and its Converse
GEOMETRY LESSON 7-2
Pages Exercises
1. 10
2. 7
3. 34
4. 12
5. 65
6. 8
7. No;
8. Yes; = 262.
9. Yes; = 252. ft
9 3 2 = / m m2
cm2
in.2
21. No;
22. No;
23. Yes; = 652.
24. obtuse
7-2

2. Pythagorean Theorem and its Converse
GEOMETRY LESSON 7-2
25. right
26. acute
27. right
28. obtuse
29. acute
30. obtuse
31. right
32. acute
33. obtuse
34. right
35. acute
36. 10
39. Answers may vary. Sample: Have three people hold the rope 3 units, 4 units, and 5 units apart in the shape of a triangle.
in.2
ft2 m2
in.2
in.
45. Yes; = 252, so RST is a rt. .
7-2

3. Pythagorean Theorem and its Converse
GEOMETRY LESSON 7-2
46. a. |x2 – x1|; |y2 – y1|
b. PQ2 = (x2 – x1)2 + (y2 – y1)2
c. PQ = (x2 – x1)2 + (y2 – y1)2
47. Answers may vary. Sample: Using 2 segments of length 1, construct the hyp. of the right formed by these segments. Using the hyp. found as one leg and a segment of length 1 as the other leg, construct the hyp. of the formed by those legs. Continue this process until constructing a hypotenuse of length n.
48. 29
49. 50
50. 84
51. 35
52–59. Answers may vary. Samples are given.
52. 6; 7
53. 4; 5
54. 8; 11
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4. Pythagorean Theorem and its Converse
GEOMETRY LESSON 7-2
55. 11; 12
56. 8; 10
57. 14; 16
58. 18; 19
59. 39; 42
60. a. c2
b. 2ab + (b – a)2
c. c2 = a2 + b2 km
BD2 + AC2 + BC2 cm cm cm
65. a. Answers may vary. Sample: n = 6; 12, 35, 37
b = 372
66. a. 5 in. b
c. d2 =
d. 34 in.
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5. Pythagorean Theorem and its Converse
GEOMETRY LESSON 7-2
70. Draw right FDE with legs DE of length a and EF of length b and hyp. of length x. Then a2 + b2 = x2 by the Pythagorean Thm. We are given ABC with sides of length a, b, c and a2 + b2 = c2. By subst., c2 = x2, so c = x. Since all side lengths of ABC and FDE are the same, ABC FDE by SSS. C E by CPCTC, so m C = 90. Therefore, ABC is a right .
72. 30
73. 9
74. 37
cm2 ft
78. 7; 33
79. 3; 20
80. 10
81. 3
82. 50
83. 7
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