Geometry: CHAPTER 3 ANSWERS
ASSIGNMENT #22:
p. 129-130 / 23-47 odds (no 29 or 31)
23. planes ABC, ABQ, PQR, CDS, APU, DET
25. AP , BQ , CR , FU , PU , QR , RS , TU
27.
33.
35.
37.
39.
41.
43.
45.
47.
BC , CD , DE , EF , QR , RS , ST , TU
alternate exterior angles
corresponding angles
alternate interior angles
consecutive interior angles
line p; alternate interior angles
line l; alternate exterior angles
line q; alternate interior angles
line m; consecutive interior angles
ASSIGNMENT #23:
p. 129-131 / 32-48 evens, 58, 60-62
32.
34.
36.
38.
40.
42.
44.
46.
48.
58.
p. 136-138 / 15-27 odds, 35
corresponding angles
15. 75
alternate interior angles
17. 105
alternate exterior angles
19. 105
consecutive interior angles
21. 43
line p; corresponding angles
23. 43
line m; alternate exterior angles
25. 137
line m; corresponding angles
27. 60
line l; corresponding angles
35. m1  113
Skew lines; the planes are flying in different directions and at different altitudes
STATEMENTS
REASONS
mABC  mDFE
m1  m4
mABC  m1  m2
2.
mDFE  m3  m4
1. Given
3. m1  m2  m3  m4
3. Substitution
4. m1  m2  m3  m1
4. Substitution
5. m2  m3
5. Subtraction property of equality
1.
2. Angle Addition Postulate
60. no conclusion
61. mEFG is less than 90 by the Law of Detachment
62. 4 10  12.65
ASSIGNMENT #24:
p. 136-138 / 14-38 evens (skip 28, 30, 36), 47-54 all
14.
16.
18.
20.
22.
24.
26.
32.
34.
38.
75
105
75
137
137
43
50
x  31 and y  45
m1  107
140
47. FG
48.
49.
50.
51.
52.
53.
AB , DE , FG , IJ , AE , FJ
plane CDH
BG , CH , FG , HI
56
53
Hypothesis: it rains this evening
Conclusion: I will mow the lawn tomorrow
54. Hypothesis: you eat a balanced diet
Conclusion: it will keep you healthy
ASSIGNMENT #25:
p. 142-144 / 15-37 odds, 43, 49, 50
15.
17.
19.
21.
23.
25.
27.
1
7
5
perpendicular
neither
parallel
3
6
29. 6
37.
43. x 
31. undefined
49. C
33.
35.
50. A
19
;
2
ASSIGNMENT #26:
p. 142-144 / 16-34 evens, 52-68 evens
1
2
p. 148-150 / 15-45 odds
4
3
20. parallel
1
x4
6
5
17. y  x  6
8
19. y   x  3
22. perpendicular
21. y 1  2  x  3 or y  2 x  5
24. neither
23. y  5  
9
5
28. 0
25. y  17.12  0.48  x  5 or y  0.48x  14.72
5
9
32. 3
29. y  2 x  4
16.
18. 
26.
30. 
15. y 
4
4
73
 x  12  or y   x 
5
5
5
27. y  3x  2
31. y   x  5
1
33. y   x
8
35. y  3x  5
34.
52. 49
54. 49
56.
58.
60.
62.
131
line l; corresponding angles
line q; consecutive interior angles
line q; corresponding angles
64. XZ  ZY  XY ;
66. acute
68. right
3
37. y   x  3
5
1
39. y   x  4
5
41. x  6
2
24
43. y  x 
5
5
45. y  0.05x  750
ASSIGNMENT #27:
p. 148-150 / 16-42 evens, 56-70 evens (no 66)
2
x8
3
2
1
18. y  x 
9
3
1
20. y   x  1
12
22. y  7  5  x  4 or y  5x  27
16. y 
1
1
173
 x  3 or y  x 
16
16
16
26. y  87.5  1.3  x  10 or y  1.3x  100.5
24. y  11 
28. y  x  5
1
30. y   x  6
8
32. y  3x  21
34. y  
1
9
x
2
2
36. y  6
38. y  1
1
x4
5
42. y  x  3
40. y 
56. 
58.
60.
62.
64.
68.
70.
3
2
0
47
107
49
2 and 5 ; 3 and 8
1 and 7 ; 4 and 6
ASSIGNMENT #28:
p. 155-157 / 13-41 odds (no 33)
13. a b ; If two lines are crossed by a transversal and alternate interior angles are congruent, then the lines are parallel
15. l m ; If two lines are crossed by a transversal and corresponding angles are congruent, then the lines are parallel
17. AE BF ; If two lines are crossed by a transversal and corresponding angles are congruent, then the lines are parallel
19. AC EG ; If two lines are crossed by a transversal and alternate interior angles are congruent, then the lines are parallel
21. HS JT ; If two lines are crossed by a transversal and corresponding angles are congruent, then the lines are parallel
23. KN PR ; If two lines are crossed by a transversal and consecutive interior angles are supplementary, then the lines are
parallel
25.
STATEMENTS
1. l  t , m  t
REASONS
1. Given
2. 1 and 2 are right angles
2. Definition of perpendicular
3. 1  2
3. All right angles are congruent
4. l m
4. If two lines are crossed by a transversal
and corresponding angles are
congruent, then the lines are parallel
27. 15
29. 8
31. 21.6
35.
STATEMENTS
REASONS
1. AD  CD, 1  2
1. Given
2. AD BC
2. If two lines are crossed by a transversal
and alternate interior angles are
congruent, then the lines are parallel
3. BC  CD
3. Perpendicular Transversal Theorem
37.
STATEMENTS
1.
RSP  PQR
QRS and PQR are supplementary
REASONS
1. Given
2. mRSP  mPQR
2. Definition of congruent angles
3. mR  mPQR  180
3. Definition of supplementary angles
4. mR  mRSP  180
4. Substitution
5. R and RSP are supplementary
5. Definition of supplementary angles
6. PS QR
6. If two lines are crossed by a transversal
and consecutive interior angles are
supplementary, then the lines are
parallel
39. No; the slopes are not equal
41. The 10-yard lines will be parallel because they are all perpendicular to the sideline and two or more lines perpendicular to
the same line are parallel.
ASSIGNMENT #29:
p. 155-157 / 14-40 evens (no 32), 47-56 all, 62
14. none
16. none
18. AE BF ; If two lines are crossed by a transversal and corresponding angles are congruent, then the lines are parallel
20. AC EG ; If two lines are crossed by a transversal and consecutive interior angles are supplementary, then the lines are
parallel
22. HS JT ; If two lines are crossed by a transversal and alternate interior angles are congruent, then the lines are parallel
24.
26.
28.
30.
34.
HS JT ; If two lines are perpendicular to the same line, then the lines are parallel
16
13
9
STATEMENTS
REASONS
1. 2  1, 1  3
1. Given
2. 2  3
2. Transitive Property of Congruence
3. ST UV
3. If two lines are crossed by a transversal
and alternate interior angles are
congruent, then the lines are parallel
36.
STATEMENTS
1.
JM KN
1  2, 3  4
REASONS
1. Given
2. 1  3
2. If two parallel lines are crossed by a
transversal, then corresponding angles
are congruent
3. 2  4
3. Substitution
4. KM
4. If two lines are crossed by a transversal
and corresponding angles are
congruent, then the lines are parallel
LN
38. Yes; the slopes are equal
40. When he measures the angle the each picket makes with the 2 by 4, he is measuring corresponding angles. When all of the
corresponding angles are congruent, the pickets must be parallel.
47. y  0.3x  6
1
x  14
3
1
19
49. y   x 
2
2
50. y  2 x  9
48. y 
51. 
52. 0
5
4
53. 1
1
2
55. undefined
54.
4
5
62. 13
56.
p. 162-164 / 11-29 odds (no 23)
11.
13.
15.
17.
; d 3
19. 4
21. 5  2.236
25.
; d 1
27.
; d  13  3.606
29. It is everywhere equidistant.
ASSIGNMENT #30:
p. 162-164 / 12-26 evens (no 18, 24), 36-43 all
12.
14.
16.
20. 6
22. 17  4.123
; d  5  2.236
26.
36. DE CF ; If two lines are crossed by a transversal and alternate interior angles are congruent, then the lines are parallel
37. DA EF ; If two lines are crossed by a transversal and corresponding angles are congruent, then the lines are parallel
38. none
1
39. y  x  3
2
40. y   x  5
2
x2
3
42. y  2 x  6
41. y 
43. y 
2
11
x
3
3
ASSIGNMENT #31:
p. 171 / 1-25 all
1
Sample answer: y   x  1 NOTE: Your slope MUST be the same!
3
2. Sample answer: If two lines are crossed by a transversal and alternate interior angles are congruent, then the lines are
parallel
3. 2 and 6
4. 116
5. 64
6. 64
7. 116
8. 116
9. 64
10. 116
11. 64
1.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
45
105
105
75
75
105
20  4.472
23. 18  4.423
24. about 2.83 miles
25. B