Geometry-PLPA ~1~ NJCTL.org 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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Geometry-PLPA ~1~ NJCTL.org
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
Geometry-PLPA ~2~ NJCTL.org
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 ~3~ NJCTL.org
Congruence, Distance & Length: CLASSWORK
41. Given: RV = 24
SU = 8
RS = ST = TU
RS = ?
42. Given: RV = 24
SU = 8
RS = ST = TU
UV = ?
43. Given: RV = 37
RS = TU
UV = 9
ST + UV = 15
ST = ?
RS = ?
SU = ?
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 FX =
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 ~4~ NJCTL.org
Congruence, Distance & Length: HOMEWORK
48. RV = 36 50. RV = 29
TV = 12 ST = UV ST = ?
ST = TU = UV RS = 7 RS = ?
UV = ? RS + ST = 16 RT = ?
49. RV = 36 51. RV = 27
TV = 12 SU = 6
ST = TU = UV ST = TU = UV
RS = ? RS = ?, RU = ?
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) b)
Geometry-PLPA ~5~ NJCTL.org
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) b)
Geometry-PLPA ~6~ NJCTL.org
Angle Addition Postulate: CLASSWORK – For #59-63, find the missing angle measure.
#106#107
#108
#109 #110
111. 112.
113.
59. 60.
61.
62. 63.
64. 65.
66.
Geometry-PLPA ~7~ NJCTL.org
Angle Addition Postulate: HOMEWORK – For #67-71, find the missing angle measure.
72.
73.
74.
67. 68.
69.
70.
71.
Geometry-PLPA ~8~ 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 ~9~ NJCTL.org
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 ~10~ NJCTL.org
Angles – Proofs of Special Angles: HOMEWORK
Find the measures of the missing angles.
101. 102.
Find the value of x.
103. 104. 105.
106. 107. 108.
33°65
4
Geometry-PLPA ~11~ 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. 116.
Geometry-PLPA ~12~ NJCTL.org
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. 124.
Geometry-PLPA ~13~ NJCTL.org
Angles – Locus & Angle Constructions: CLASSWORK
125. Construct a congruent angle for each figure below.
a)
B
A
C
b)
E
D
F
Angles – Locus & Angle Constructions: HOMEWORK
126. Construct a congruent angle for each figure below.