Points, Lines, Planes, & Angles
Points & Lines: CLASSWORK
1. Name three collinear points on line q and on line s
2. Name 4 sets of non-collinear points
3. Name the opposite rays on line q and on line s
4. How many points are marked on line q?
5. How many points are there on line q?
Points & Lines: HOMEWORK
6. Name three collinear points on line o
7. Name 4 sets of collinear points
8. Name two opposite rays on line j with endpoint R
9. Which 4 points are collinear? What line are they on?
10. How many points are there on line j?
Points & Lines: CLASSWORK
Name a point that is collinear with the given points
11. O and S
12. P and R
13. U and T
14. U and S
15. Name 3 points non-collinear with T and V
Points & Lines: HOMEWORK
16. Q and S
17. T and R
18. U and V
19. P and S
20. Name 3 points non-collinear with T and U
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Planes: CLASSWORK
21. Name a point that is coplanar with A, E, and J
22. Name a point that is coplanar with A, C, and I
23. Name all the points that are noncoplanar with A, C, and D
24. Name all the points that are noncoplanar with F, H, and E
25. Where do plane ACH and plane IDC intersect?
26. Where do planes ACH, AFJ, and ACD intersect?
Planes: HOMEWORK
27. Name a point that is coplanar with E, D, and I
28. Name a point that is coplanar with A, E, and J
29. Name all the points that are noncoplanar with A, F, and H
30. Name all the points that are noncoplanar with A, F, and D
31. Where do plane JED and plane FHI intersect?
32. Where so planes AED, CHI, and JED intersect?
Congruence, Distance & Length: CLASSWORK
33. Find the distance between point K and point M
34. Find the distance between point P and point L
35. Find the distance between point O and Point N
36. Find the distance between point L and point N
Congruence, Distance & Length: HOMEWORK
37. Find the distance between point N and point K
38. Find the distance between point Q and point L
39. Find the distance between point L and point P
40. Find the distance between point K and point Q
Geometry-PLPA
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Congruence, Distance & Length: CLASSWORK
41. Given: RV = 24
SU = 8
RS = ST = TU
RS = ?
43. Given: RV = 37
RS = TU
UV = 9
ST + UV = 15
ST = ?
RS = ?
SU = ?
42. Given: RV = 24
SU = 8
RS = ST = TU
UV = ?
44. Given: RV = 25
RT = 6
RS = ST = TU
UV = 3x +1
x=?
45. Points F, X, and D are collinear, with F between X and D. Draw a diagram and solve for X, if
2x+13, FD = 7x-6, and XD = 2x+70.
46. P, A, and Z are collinear. Z is between P and A. Draw a diagram and solve for x, given:
ZP = 6x-13, ZA = 9x+27, and AP = 3x +74.
47. A, B, and C are collinear with A between B and C. Draw a diagram and solve for x, given:
AC = 17x – 69, AB = 6x+23, and BC = 25x-50.
Geometry-PLPA
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FX =
Congruence, Distance & Length: HOMEWORK
48. RV = 36
TV = 12
ST = TU = UV
UV = ?
50. RV = 29
ST = UV
RS = 7
RS + ST = 16
49. RV = 36
TV = 12
ST = TU = UV
RS = ?
51. RV = 27
SU = 6
ST = TU = UV
RS = ?, RU = ?
ST = ?
RS = ?
RT = ?
52. D, V, and U are collinear with U between D and V. Draw a diagram and solve for x, given:
DU = 4x+5, VU = 3x-8, and VD = 10x-30.
53. P, R, and F are collinear with F between R and P. Draw a diagram and solve for x, given: FR = 7x-8,
FP = 4x+20, and PR = 13x – 6.
54. W, S, and X are collinear with W between X and S. Draw a diagram and solve for x, given: XW = 3x+5,
SW = 7x-18, and XS = 6x+19.
Constructions & Loci: CLASSWORK
55. Draw a circle for each given radius length in the figures below.
a)
Geometry-PLPA
b)
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56. Construct congruent segments for each segment given below. Hint: remember to draw a longer line in
any direction to start constructing your congruent segment.
a)
b)
Constructions & Loci: HOMEWORK
57. Draw a circle for each given radius length in the figures below.
a)
b)
58. Construct congruent segments for each segment given below. Hint: remember to draw a longer line
in any direction to start constructing your congruent segment.
a)
Geometry-PLPA
b)
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Angle Addition Postulate: CLASSWORK – For #59-63, find the missing angle measure.
59.
#106
60. #107
62.#109
63.
#110
64.
111.
61.#108
65.
112.
66.
113.
Geometry-PLPA
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Angle Addition Postulate: HOMEWORK – For #67-71, find the missing angle measure.
67.
68.
69.
70.
72.
71.
73.
74.
Geometry-PLPA
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NJCTL.org
Angles – Special Angle Pairs: CLASSWORK
75. True/False Complementary angles form a right angle
76. True/False: Supplementary angles form a straight angle
77. Two angles are complementary. One of the angles is 17°, what is the measure of the other angle?
78. Two angles are supplementary. One of the angles is 97°, what is the measure of the other angle?
79. Two angles are supplementary. One of the angles is three times the size of the other, what is the
measure of the larger angle?
80. An angle x is 20° more than its complement. What is the angle’s measure?
81. An angle x is 66° less than its complement. What is the angle’s measure?
82. An angle x is 46° more than its supplement. What is the angle’s measure?
83. An angle x is 18° less than its supplement. What is the angle’s measure?
Angles – Special Angle Pairs: HOMEWORK
84. True/False: Supplementary angles always sum to 90°
85. True/False: Complementary angles sometimes form straight angles
86. Two angles are complementary. One of the angles is 57°, what is the measure of the other angle?
87. Two angles are supplementary. One of the angles is 43°, what is the measure of the other angle?
88. Two angles are supplementary. One of the angles is five times the smaller angle, what is the measure
of the larger angle?
89. An angle is 74° more than its complement. What is the angle’s measure?
90. An angle is 36° less than its complement. What is the angle’s measure?
91. An angle is 88° more than its supplement. What is the angle’s measure?
92. An angle is 16° less than its supplement. What is the angle’s measure?
Geometry-PLPA
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Angles – Proofs of Special Angles: CLASSWORK
Find the measures of the missing angles.
93.
94.
Find the value of the variables.
95.
96.
97.
98.
99.
100.
Geometry-PLPA
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Angles – Proofs of Special Angles: HOMEWORK
Find the measures of the missing angles.
101.
102.
33° 4
5 6
Find the value of x.
103.
104.
105.
106.
107.
108.
Geometry-PLPA
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NJCTL.org
Angles – Angle Bisector: CLASSWORK
Given that ray BD bisects ∠ ABC in the figure below, find the missing measurements. Note: the questions
are NOT related.
Given that ray JL bisects ∠ IJK in the figure below, find the value of x.
113.
114.
115.
Geometry-PLPA
116.
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Angles – Angle Bisector: HOMEWORK
Given that ray RT bisects ∠ QRS in the figure below, find the missing measurements. Note: the questions
are NOT related.
R
Q
S
T
Given that ray JL bisects ∠ IJK in the figure below, find the value of x.
121.
122.
123.
Geometry-PLPA
124.
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NJCTL.org
Angles – Locus & Angle Constructions: CLASSWORK
125. Construct a congruent angle for each figure below.
a)
A
B
C
b)
D
E
F
Angles – Locus & Angle Constructions: HOMEWORK
126. Construct a congruent angle for each figure below.
a)
H
G
I
b)
K
J
L
Geometry-PLPA
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Angles –Angle Bisectors & Constructions: CLASSWORK
127. Construct the angle bisector of each angle below using any construction method of your choice.
a)
b)
Angles –Angle Bisectors & Constructions: HOMEWORK
128. Construct the angle bisector of each angle below using any construction method of your choice.
a)
b)
Geometry-PLPA
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Points, Lines, Planes and Angle
Review Multiple Choice
129.
Intersecting lines are _________________ non-coplanar
a.always
b.sometimes
c.never
130.
Two non-parallel lines _________________ intersect at one point.
a.always
b.sometimes
c.never
131.
Two points are _________________ collinear.
a.always
b.sometimes
c.never
132.
Three points are _________________ collinear.
a.always
b.sometimes
c.never
133.
Three points are _________________ coplanar.
a.always
b.sometimes
c.never
134.
Four points are _________________ coplanar.
a.always
b.sometimes
c.never
135.
When two planes intersect, they do so:
a.at a point
b.along a line
c.along a plane
136.
All points along a line are _________________ collinear.
a.always
b.sometimes
c.never
137.
Opposite rays (circle all that apply):
a.are collinear
b.have the same endpoint
c.sometimes overlap
d.form a straight angle
Geometry-PLPA
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138.
If points A, B, C are collinear with C between A and B, the segment addition postulate is:
a.AB + BC = AC
b.BA + CB = AC
c.BC + CA = AB
d.BC + AC = CA
139.
Points J, K and L are collinear with J between L and K. If KJ = 2x - 3, LK = 9x + 7 and LJ = 4x - 8,
solve for x:
a.6
b.-6
c.-4
d.4
140.
Two rays that have a common endpoint could form (check all that apply):
a. an angle
b. a straight line
c. opposite rays
d. a vertex
141.
Acute angles are:
a. less than 90⁰
b. greater than 90⁰ but less than 180⁰
c. equal to 180⁰
d. greater than 180⁰ but less than 360⁰
142.
Obtuse angles are:
a. less than 90⁰
b. greater than 90⁰ but less than 180⁰
c. equal to 180⁰
d. greater than 180⁰ but less than 360⁰
143.
Adjacent angles (circle all that apply):
a. have a common side
b. sum to 90⁰
c. share a common vertex
d. are less than 90⁰
144.
Complementary angles (circle all that apply):
a. sum to 90⁰
b. sum to 180⁰
c. form a straight angle
d. form a right angle
e. are adjacent angles
Geometry-PLPA
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145.
Supplementary angles (circle all that apply):
a. sum to 90⁰
b. sum to 180⁰
c. form a straight angle
d. form a right angle
e. are adjacent angles
146.
An angle is 34⁰ more than its compliment. What is the measure of the angle?
a. 64⁰
b. 124⁰
c. 28⁰
d. 62⁰
147.
An angle is 58⁰ less than its supplement. What is the measure of the angle?
a. 33⁰
b. 61⁰
c. 123⁰
d. 154⁰
148.
Find the measures of the angles to the right.
a.
b.
c.
d.
1 113°
2 3
149.
Find the value of x in the figure to the right.
a. ½
b. 9
(x+19)°
c. 12
d. 24
(5x+17)°
150.
An angle bisector (circle all that apply):
a. forms two congruent angles
b. is a line or a ray
c. is equidistant from the sides of the angle
d. forms two adjacent angles
151.
The statement, "the whole is the sum of the parts" refers to (circle all that apply):
a. complementary angles
b. the segment addition postulate
c. adjacent angles
d. the angle addition postulate
Geometry-PLPA
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Points, Lines, Planes and Angles
Review Constructed Response
152. Points B, D, F, H and J are collinear and are in the following order

D is between J and B

F is between D and J

B is between F and H

JH = 47, FB = 12, FD = DB = BH and JF = 3x - 7
Draw a diagram of the points, solve for x and solve for JF.
153.An angle is 36⁰ less than its complement. What is the measure of the angle?
154. An angle is 102⁰ more than its supplement. What is the measure of the angle?
155. If F is in the interior of ∠APB and m∠APB = (5x +11)⁰, m∠APF = (6x - 6)⁰ and m∠FPB = (9x +- 23)⁰:
 Draw a diagram
 Solve for x
 What is the m∠APF and m∠APB?
Geometry-PLPA
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Answer Key
1. KLI & HLJ
2. HLK, HLI, KLJ, ILJ
3. LK, LI, LJ, LH
4. 3
5. Infinite
6. VRS
7. QVW, TUR, QUS, VRS
8. RW, RU
9. TURW, j
10. Infinite
11. Q
12. Q
13. R
14. P
15. PSOU or R
16. O
17. U
18. O
19. U
20. POSQ or V
21. F
22. J
23. FHJI
24. ACJI
25. CH
26. A
27. J
28. F
29. EDJI
30. CHEJ
31. JI
32. D
33. 5
34. 12
35. 4
36. 3
37. 6
38. 14
39. 12
40. 17
41. 4
42. 12
43. ST=6 RS=11 SU=17
44. 5
45. 9
Geometry-PLPA
46. 5
47. 2
48. 6
49. 18
50. ST = 9 RS = 7 RT = 16
51. RS = 18 RU = 24
52. 9
53. 9
54. 8
55. Check Constructions
56. Check Constructions
57. Check Constructions
58. Check Constructions
59. 26⁰
60. 72⁰
61. 23⁰
62. 123⁰
63. 193⁰
64. 15
65. 3
66. 3
67. 71⁰
68. 14⁰
69. 17⁰
70. 57⁰
71. 33⁰
72. 5.8666...
73. 2
74. 7
75. True
76. True
77. 73⁰
78. 83⁰
79. 135⁰
80. 55⁰
81. 12⁰
82. 113⁰
83. 81⁰
84. False
85. False
86. 33⁰
87. 137⁰
88. 150⁰
89. 82⁰
~19~
90. 27⁰
91. 134⁰
92. 82⁰
93. 63o, 117o, 63o
94. 128o, 128o, 52o
95. x = 17
96. x = 7
97. x = 16
98. x = 13
99. x = 16 & y = 6
100.
x=4&y=6
101.
126o, 54o, 54o
102.
147o, 147o, 33o
103.
x = 11
104.
x=7
105.
x = 13
106.
x = 10
107.
x = 20 & y = 5
108.
x = 10 & y = 20
109.
39o, 39o
110.
44o, 44o
111.
112o, 56o
112.
46o, 92o
113.
x = 24
114.
x=6
115.
x = 10
116.
x=9
117.
48o, 96o
118.
88o, 176o
119.
83o, 83o
120.
53o, 53o
121.
x = 10
122.
x = 21
123.
x=8
124.
x = 4.5
125.
Check
Constructions
126.
Check
Constructions
127.
Check
Constructions
128.
Check
Constructions
NJCTL.org
Review Answer Key Multiple Choice
129. C
130. A
131. A
132. B
133. A
134. B
135. B
136. A
137. A, B, D
138. C
139. B
140. A, B, C, D
141. A
142. B
143. A, C
144. A, D
145. B, C
146. D
147. B
148. C
149. D
150. A, B, C, D
151. B, D
Geometry-PLPA
Review Answer Key Constructed Response
152.
x = 12 JF = 29
153.
x = 27⁰
154.
x = 141⁰
155.
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