points, lines, planes, & angles -...

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


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


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.


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)


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)


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.


Angle Addition Postulate: HOMEWORK – For #67-71, find the missing angle measure.

72.

73.

74.

67. 68.

69.

70.

71.


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?


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.


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


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.


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.


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.

a)

G

H

I

b)

J

K

L


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)


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


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


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.

149. Find the value of x in the figure to the right.

a. ½

b. 9

c. 12

d. 24

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

32

1 113°

(x+19)°

(5x+17)°


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?


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

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




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

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


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

Review Answer Key Constructed Response

152. x = 12 JF = 29

153. x = 27⁰

154. x = 141⁰

155. m∠APF = 18⁰

m∠APB = 31⁰

points, lines, planes, & angles -...

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