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12. (a) Prove that ABCD is a parallelogram (since opposite sides are congruent) and has a rt. j. 1 (b) The point (3, 22) is the midpoint of each diagonal. (c) Yes, since the midpoint of each diagonal is their common point. 13. (a) D(3, 2), (12,1); (b) E(0, 2), (3, 1); (c) no, since the midpoint of each median is not a common point 14. (a) 5; (b) 6; (c) 10; (d) 12; (e) 5.4; (f) 7.5; (g) 9; (h) a 15. (a) 3, 3, 6; (b) 4, 14, 18; (c) 1, 3, 4; (d) a, 2a, 3a 16. (a) 13; (b) 5; (c) 15; (d) 5; (e) 10; (f) 15; (g) 3 22; (h) 5 22; (i) 210; (j) 2 25; (k) 4; (l) a 22 18. (a) ^ABC; (b) ^DEF; (c) ^GHJ; (d) ^KLM is not a rt. ^ 19. (a) 5 22; (b) 25; (c) 265 21. (a) 10; (b) 5; (c) 5 22; (d) 13; (e) 4; (f) 3 22. (a) on; (b) on; (c) outside; (d) on; (e) inside; (f) inside; (g) on 23. (a) 5; (b) 9; (c) 5; (d) 3; (e) 2; (f) 1; (g) 5; (h) 2; (i) 3; (j) 2; (k) 1; (l) 1 2 24. (a) 3; (b) 4; (c) (o) 4; (p) 8
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(d) 7; (e) 5; (f) 0; (g) 3; (h) 5; (i) 4; (j)
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(k) 1; (l) 2; (m) 5; (n) 6;
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25. (a) 72 ; (b) 18 ; (c) 68 ; (d) 22 ; (e) 45 ; (f) 0 26. (a) 0.0875; (b) 0.3057; (c) 0.3640; (d) 0.7002; (e) 1; (f) 3.2709; (g) 11.430 27. (a) 0 ; (b) 25 ; (c) 45 ; (d) 55 ; (e) 7 ; (f) 27 ; (g) 37 ; (h) 53 ; (i) 66 28. (a) BC, BD, AD, AE; (b) BF, CF, DE; (c) AF, CD; (d) AB, EF 29. (a) 0; (b) no slope; (c) 5; (d) 5; (e) 0.5; (f) 0.0005 30. (a) 0; (b) no slope; (c) no slope; (d) 0; (e) 5; (f) 1; (g) 2 31. (a) 3; (b) 7; (c) 1; (d) 6 2 3 32. (a) 2; (b) 1; (c) 34. (a) 35. (a) 36. (a)
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(e) 10; (f) 1; (g) 4; (h) 13; (i) no slope; (j) 0
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33. (a) 0; (b) 2; (c) 3; (d) 1 (b) 3; (c) (b) 1; (c) 6 4
5 2 3 2
(b) 1; (c) 2; (d) 1
37. (a) and (b) 38. (a) 19; (b) 9; (c) 2 39. (a) x (g) y 40. (a) x 41. (a) x (g) x
1 5; (b) y 32; (c) y 3 and y 4; (h) x 1; (i) x 9
3; (d) y 5; (e) x
5; (e) x 3 y
4 and x
4; (f) x
5 and x
6; (b) y y; (b) y y and x
5; (c) x
6; (d) x
6; (f) y 10; (e) x
x 5; (c) x y 4; (d) y x y; (h) x y 5
12; (f) x y
2 or y x
42. (a) line having y-intercept 5, slope 2; (b) line passing through (2, 3), slope 4; 5 (c) line passing through ( 2, 3), slope 4; (d) line passing through origin, slope 1; 2 1 (e) line having y-intercept 7, slope 1; (f) line passing through origin, slope 3 43. (a) y 44. (a) y (f) y 4x; (b) y 2x; (c) y
3 2x
or 2y
1 3x
3x; (d) y 1 or 3y
2 5x
or 5y
2x; (e) y 3x
0 4x 3;
4x 5; (b) y 3x 2x or y 2x 0
2; (c) y
x 3; (d) y
8; (e) y
y 45. (a) x (d) y x
4 1 7
2 or y 2 or y
1 2x
y 2; (b) x
2 or y
7; (c) x
2 or y
2x 7 3; (c) y x 2 1 3; (d) y x 2 1 y2 1 ; (e) y 3 16; (c) x2 y2 9y2 144 4; (d) x2 y2
46. (a) y
4x; (b) y
2x y2 64 and x2 y2 4
47. (a) circle with center at origin and radius 7; (b) x2 48. (a) x2 50. (a) x
4 3;
25; (b) x2 (c) 2; (d) 23 16; (b) x2 5; (f) x2
y2 y2 y2
81; (c) x2 121; (c) x2
y2 y2 4y2
4 or x2
49. (a) 3; (b) y (e) x2
or 9x2
or 4x2
or 4x2
51. (a) 10; (b) 10; (c) 20; (d) 20; (e) 7; (f) 25 52. (a) 16; (b) 12; (c) 20; (d) 24 53. (a) 10; (b) 12; (c) 22 54. (a) 5; (b) 13; (c) 72 55. (a) 6; (b) 10; (c) 1.2 56. (a) 15; (b) 49; (c) 53 57. (a) 30; (b) 49; (c) 88; (d) 24; (e) 16; (f) 18
13
1. (a) 2. (a) 3. (a) 5. (a) ; (b) ; (b) ; (b) ; (b) ; (c) ; (c) ; (c) ; (c) ; (d) ; (d) ; (d) ; (d) ; (e) ; (f) ; (e) ; (f)
4. (a) more; (b) less 6. (c), (d), and (e) 7. (a) 5 to 7; (b) 6 to 10; (c) 4 to 10; (d) 3 to 9; (e) 2 to 8; ( f ) 1 to 13 8. (a) jB, jA, jC; (b) DF, EF, DE; (c) j3, j2, j1 9. (a) mjBAC mjACD; (b) AB BC 10. (a) BC, AB, AC; (b) jBOC, jAOB, jAOC; (c) AD, AB > CD, BC; (d) OG, OH, OJ