2
46. DF = 10
47. DH = 9
48. FG = 8
49. GH = 4
50. DF = 11
51. We should have DG + GH = DH ,
but 12 + 3 ≠ 18 .
52. We should have DG + GH = DH ,
but 16 + 6 ≠ 22 .
53. LE = 20, ED = 20, LD = 40
54. RA = 1.5, AO = 1.5, RO = 3
55.
56.
AD ≅ JP
AL ≅ LP ≅ DJ
BT ≅ AZ
TC ≅ CA ≅ BZ
57. a.) 3.25in b.) 2.9in
1
58. 17
30
59. 26.7in
60. 5, 6, and 12
61. 16in,9in,18in
62. H = -5, L = -2, J = 4
63. B
64. 6
65. yes
66. HS
67. 3 23 in
68.
c.) 6.15in
Venus – obtuse
Saturn – obtuse
Jupiter – acute
12. 90 o
13. 180 o
14. 45 o
15. 135 o
16. 90 o
17. 120 o
18. 180 o
19. 90 o
20. ∠ABE , ∠ABD -acute,
∠CBE , ∠CBD -obtuse, ∠ABC -straight
21. ∠ABC -acute, ∠BCA -acute,
∠CAB -right
22.
∠CAD, ∠BAD, ∠ABD, ∠ADB, ∠ACD
-acute, ∠CDA -obtuse, ∠CAB -right
23.
24. No
25.
Section 2: More About Angles
1. vertical, adjacent, supplementary
2. acute
3. transversal
4. obtuse
5. perpendicular
6. same-side angles
7. F
8. F
9. F
10. F
11. Mars – right
26.
2
46. DF = 10
47. DH = 9
48. FG = 8
49. GH = 4
50. DF = 11
51. We should have DG + GH = DH ,
but 12 + 3 ≠ 18 .
52. We should have DG + GH = DH ,
but 16 + 6 ≠ 22 .
53. LE = 20, ED = 20, LD = 40
54. RA = 1.5, AO = 1.5, RO = 3
55.
56.
AD ≅ JP
AL ≅ LP ≅ DJ
BT ≅ AZ
TC ≅ CA ≅ BZ
57. a.) 3.25in b.) 2.9in
1
58. 17
30
59. 26.7in
60. 5, 6, and 12
61. 16in,9in,18in
62. H = -5, L = -2, J = 4
63. B
64. 6
65. yes
66. HS
67. 3 23 in
68.
c.) 6.15in
Venus – obtuse
Saturn – obtuse
Jupiter – acute
12. 90 o
13. 180 o
14. 45 o
15. 135 o
16. 90 o
17. 120 o
18. 180 o
19. 90 o
20. ∠ABE , ∠ABD -acute,
∠CBE , ∠CBD -obtuse, ∠ABC -straight
21. ∠ABC -acute, ∠BCA -acute,
∠CAB -right
22.
∠CAD, ∠BAD, ∠ABD, ∠ADB, ∠ACD
-acute, ∠CDA -obtuse, ∠CAB -right
23.
24. No
25.
Section 2: More About Angles
1. vertical, adjacent, supplementary
2. acute
3. transversal
4. obtuse
5. perpendicular
6. same-side angles
7. F
8. F
9. F
10. F
11. Mars – right
26.
3
27.
a.) 130 o − obtuse
b.) 100 o − obtuse
c.) 125 o − obtuse
d.) 85 o − acute
e.) 35 o − acute
28. ∠a and ∠c , ∠b and ∠d
29. ∠a and ∠d , ∠a and ∠b ,
∠b and ∠c , ∠c and ∠d
m(∠a) = m(∠c) = 50 o ,
30.
m(∠b) = m(∠d ) = 130 o
31.
m(∠a) = m(∠c) = 60 o ,
m(∠b) = m(∠d ) = 120 o
32. Yes, they could both be 45 o ; yes,
they could both be 90 o .
33. a.) x = 24 , b.) x = 32 , c.) x = 44
34. a) x = -32, b) x = 10
c) x = 11 2 3
35. two congruent, 74 o
36. two, 28.5°
37. two congruent, 53.4 o
o
38. two, 39 3
8
39. a.) neither, b.) complementary,
c.) supplementary, d.) neither
40. 51o
41. 141o
42. 68 o
43. 9.6 o
44. 85.85 o
o
45. 21 23
46. 75 o
47. 157.5 o
48. 70 o
49. 52 o
50. If two numbers are both more than
90, they will add up to be more than 180.
51. If two numbers are both less than 90,
they cannot add up to 180.
52. ∠ADE
53. ∠BCE , ∠ABE , ∠BAD, ∠ACD
54.
m(∠ACD) = m(∠BCE ) = 108 o ,
m(∠DCE ) = 72 o
55. ∠BAC and ∠CAD ,
∠ABC and ∠CBE ,
∠ADC and ∠CDE
56. ∠ACD and ∠BCE ,
∠ACB and ∠DCE
57. ∠ADC and ∠CDE
58. ∠CED and ∠CAD
59. ∠ACB and ∠BCE
60. not possible
61. AD and DE
62. x = 8
63. x = 26
64.
65.
66. yes,
67. All obtuse angles are 107 o and all
acute 73 o .
68. All obtuse angles are 97 o and all
acute angles are 83 o .
69. All obtuse angles are 110 o and all
acute angles are 70 o .
70.
71. H, F, N, E, Z
4
72. H, F, T, E
73. F, E
74. X
75. A, H, F, N, E, Z
76. A, H, F, E, X
Section 3: Triangles
1. isosceles
2. obtuse triangle
3. right triangle
4. Pythagorean triple
5. hypotenuse
6. vertices
7. T
8. F
9. T
10. F
11. ∆XYZ
12. X, Y, Z
13. XY , YZ , ZX
14. ∠YXZ , ∠XYZ , ∠YZX
15. isosceles
16. acute triangle
17. ∠Z
18. ∠Y
19. scalene triangle
20. isosceles triangle
21. obtuse triangle
22. equilateral/equiangular triangle
23. right triangle
24. acute
25. isosceles right triangle
26. obtuse triangle
27. b and c are impossible
28. obtuse isosceles triangle
29. right isosceles triangle
30. right triangle
31. isosceles triangle
32. acute isosceles triangle
33. ∆DJR - acute isosceles triangle
∆SJR - obtuse scalene triangle
∆DRS - right scalene triangle
34. ∆GHM - obtuse isosceles triangle
∆GHT - not possible
∆MHT - right scalene triangle
35.
36.
37.
38.
39.
40.
41.
68 o
20 o
90 o
45 o
76.9 o
o
63 158
42.
43.
44.
45.
46.
47.
48.
49.
60 o
35 o ,58 o ,87 o
55 o ,82.5 o ,42.5 o
36 o ,36 o ,108 o
27 o
x = 19
x = 33
o
38 45
50. m(∠A) = 65 o , m(∠ACB) = 80 o
51. m(∠B) = 75 o , m(∠BLS ) = 150 o
52. m(∠2) = 98 o , m(∠3) = 135 o ,
m(∠5) = 127 o , m(∠6) = 127 o
53.
54.
55. c = 10cm
56. B = 7in.