Chapter 3 Parallel and Perpendicular Lines Name_______________________________

Geometry

For 1-5, use the figure below. The two pentagons are parallel and all of the rectangular sides are

perpendicular to both of them.

1. Find two pairs of skew lines.

2. List a pair of parallel lines.

3. List a pair of perpendicular lines.

4. For , how many perpendicular lines pass through point V? What line is this?

5. For , how many parallel lines pass through point D? What line is this?

For 6-12, use the picture below.

6. What is the corresponding angle to ∠4?

7. What is the alternate interior angle with ∠5?

8. What is the corresponding angle to ∠8?

9. What is the alternate exterior angle with ∠7?

10. What is the alternate interior angle with ∠4?

11. What is the same side interior angle with ∠3?

12. What is the corresponding angle to ∠1?

For 13-16, use the picture below.

13. If ∠ , what other angles do you know?

14. If ∠ , what other angles do you know?

15. If t ⊥ l, is t ⊥ m? Why or why not?

16. Is l ∥ m? Why or why not?

17. Draw a pair of parallel lines using your ruler. Describe how you did this.

18. Draw a pair of perpendicular lines using your ruler. Describe your method.

For 19-21, think of examples of each of the following in nature.

19. Parallel lines or planes.

20. Perpendicular lines or planes.

21. Skew lines.

22. Write the equations of two lines parallel to y = 3.

23. Write the equations of two lines perpendicular to y = 5.

24. What is the relationship between the two lines you found for #23?

25. Plot the points A(2, -5), B(-3, 1), C(0, 4), and D(-5, 10). Draw the lines and . What

are the slopes of these lines? What is the geometric relationship between these lines?

26. Plot the points A(2, 1), B(7, -2), C(2, -2), and D(5, 3). Draw the lines and . What

are the slopes of these lines? What is the geometric relationship between these lines?

27. Based on what you discovered in #25 and #26, can you make a conjecture about the

slopes of parallel and perpendicular lines?

For 28 & 29, find the equation of the line that is parallel to the given line and passes through

(5, -1).

28.

29.

For 30 & 31, find the equation of the line that is perpendicular to the given line and passes

through (2, 3).

30.

31.

For 32-38, determine if each angle pair below is congruent, supplementary, or neither.

32. ∠1 and ∠7

33. ∠4 and ∠2

34. ∠6 and ∠3

35. ∠5 and ∠8

36. ∠1 and ∠6

37. ∠4 and ∠6

38. ∠2 and ∠3

For 39-47, determine if the angle pairs below are: Corresponding Angles, Alternate Interior

Angles, Alternate Exterior Angles, Same Side Interior Angles, Vertical Angles, Linear Pair, or

None.

39. ∠2 and ∠13

40. ∠7 and ∠12

41. ∠1 and ∠11

42. ∠6 and ∠10

43. ∠14 and ∠9

44. ∠3 and ∠11

45. ∠4 and ∠15

46. ∠5 and ∠16

47. List all angles congruent to ∠8

For 48-51, find the values of x and y.

48.

49.

50.

51.

For 52-56, use the picture below. Find the value of x and/or y.

52. ∠ , ∠

53. ∠ , ∠

54. ∠ , ∠

55. ∠ , ∠

56. ∠ , ∠

57. Find the measures of all the numbered angles in the figure below.

For 58 & 59, find the values of x and y.

58.

59.

For 60-65, use the given information to determine which lines are parallel. If there are none,

write none. Consider each questions individually.

60. ∠ ∠

61. ∠BCE and ∠BAF are supplementary.

62. ∠ ∠

63. ∠ ∠

64. ∠ ∠

65. ∠ ∠

For 66-72, find the measure of the lettered angles below.

66. ∠

67. ∠

68. ∠

69. ∠

70. ∠

71. ∠

72. ∠

For 73-77, what does x have to measure to make the lines parallel?

73. ∠ and ∠

74. ∠ and ∠

75. ∠ and ∠

76. ∠ and ∠

77. ∠ and ∠

78. What is wrong in the following diagram, given that the two lines are parallel?

For 79-87, find the measure for ∠1.

79.

80.

81.

82.

83.

84.

85.

86.

87.

For 88-91, use the picture below.

88. Find ∠

89. Find ∠

90. Find ∠

91. Find ∠

For 92-95, determine if l ⊥ m.

92.

93.

94.

95.

For 96-103, use the picture below.

96. Find ∠ .

97. Find ∠ .

98. Find ∠ .

99. Find ∠ .

100. Find ∠ .

101. Find ∠ .

102. Find ∠ .

103. Find ∠ .

For 104-109, find the value of x.

104.

105.

106.

107.

108.

109.

For 110-115, find the slope between the two given points.

110. (4, -1) and (-2, -3)

111. (-9, 5) and (-6, 2)

112. (7, 2) and (-7, -2)

113. (-6, 0) and (-1, -10)

114. (1, -2) and (3, 6)

115. (-4, 5) and (-4, -3)

For 116-123, determine if each pair of lines are parallel, perpendicular, or neither. Then graph

each pair on the same set of axes.

116. and

117. and

118. and

119. and

120. and

121. and

122. and

123. and

For 124-129, determine the equation of the line that is parallel to the given line, through the

given point.

124. ; (-2, 3)

125.

; (9, 1)

126. ; (-16, -2)

127. ; (8, -11)

128. ; (3, 7)

129. ; (9, -1)

For 130-135, determine the equation of the line that is perpendicular to the given line, through

the given point.

130. ; (-6, 2)

131. ; (9, -7)

132. ; (5, 5)

133. ; (-1, 3)

134. ; (1, 8)

135. ; (0, 13)

For 136-139, find the equation of the two lines in each graph below. Then, determine if the two

lines are parallel, perpendicular, or neither.

136.

137.

138.

139.

For 140-143, use the line and point below to find

a) A parallel line, through the given point.

b) A perpendicular line, through the given point.

140.

141.

142.

143.

For 144-151, find the distance between each pair of points. Round your answer to the nearest

hundredth.

144. (4, 15) and (-2, -1)

145. (-6, 1) and (9, -11)

146. (0, 12) and (-3, 8)

147. (-8, 19) and (3, 5)

148. (3, -25) and (-10, -7)

149. (-1, 2) and (8, -9)

150. (5, -2) and (1, 3)

151. (-30, 6) and (-23, 0)

For 152-155, determine the shortest distance between the given line and point. Round your

answer to the nearest hundredth.

152.

; (5, -1)

153. ; (-7, -3)

154. ; (4, 2)

155.

; (7, 9)

For 156-159, use each graph below to determine how far apart the parallel lines are. Round your

answers to the nearest hundredth.

156.

157.

158.

159.

For 160-165, determine the shortest distance between each pair of parallel lines. Round your

answer to the nearest hundredth.

160. and

161. and

162. and

163.

and

164. and

165.

and

For 166-169, find the equation of the perpendicular bisector for each pair of points.

166. (1, 5) and (7, -7)

167. (1, -8) and (7, -6)

168. (9, 2) and (-9, -10)

169. (-7, 11) and (-3, 1)

170. The perpendicular bisector of has the equation . If D is (-3, 0), what

are the coordinates of C?

171. The perpendicular bisector of has the equation . If L is (6, -3), what

are the coordinates of M?

172. The distance between two points is 25 units. One point is (-2, 9). What is the Second

point? You may assume that the second point is made up of integers.

173. List the steps you would take to find the distance between two parallel lines, like the

two in #162.