Geometry
Name____________________________________
Chapter 3 Review
Date_____________________________________
Use the picture at right to complete the following with parallel, perpendicular or skew.
1.
AD and CB are ________________
2.
FG and AE are ________________
3.
AB and AD are ________________
4.
AB and HG are ________________
G
H
E
Name a plane parallel to FGC ________________.
6.
Name a segment parallel to EA ________________
7.
Name a segment skew to CD ________________
C
D
Use the picture above to complete the following.
5.
F
A
B
Complete with always, sometimes or never.
8.
Two lines that are perpendicular to the same line are _____________ perpendicular.
9.
Two lines that are parallel to the same line are _____________ parallel.
10.
Two lines that do not intersect are _____________ parallel.
11.
If two lines are cut by a transversal, then alternate interior angles are ___________ congruent.
12.
If two parallel lines are cut by a transversal, then corresponding angles are _____________ congruent.
13.
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are
______________ parallel.
Use the picture at right to give the special name for each pair of angles.
m
14. 6 and 4__________________________
15.
2 and 3 ________________________
16.
3 and 7 ________________________
17.
5 and 6 __________________________
18.
7 and 2 __________________________
19.
6 and 3 __________________________
t
1 2
3 4
6
5
7 8
n
7
Given l | | m , find the value of x and y.
20.
x°
21.
y°
22.
l
41°
x°
36°
y°
2x°
m
117°
l
x = ________ y = ________
(6y – 6)°
m
x = ________ y = _________
x = ________ y = _________
Find the value of x.
23.
24.
.
35o o
(2x + 8 )°
x
(3x+2)°
In each figure l | | m. Find the value of x.
t
25.
26.
l
(3x)
(x + 20)
t
(2x + 10)
m
(3x – 14)
27.
l
m
28.
(60)
(4x + 20)
l
l
m
(2y+ 10)
t
t
m
29.
Write the Corresponding Angle Postulate.
30.
Write the Converse of the Corresponding Angle Postulate.
Find the value of x that will make l || m.
31.
32.
33.
70°
2x°
4x°
15°
(6x + 2)°
l
(3x + 20)°
l
l
m
m
x°
m
Use the given information and the figure at right to determine which lines, if any, must be parallel.
34. ___________ 11  5
1 2
5 6
35. ___________ 15  1
36. ___________ 11 and 12 are supplementary
b
a
9 10 11
14 15
3 4
7 8
12 13
16 17
37. ___________ m9  m10  m17
38. ___________ 14 and 17 are supplementary
39. ___________ 11  12
Determine if AB || CD .
40. A(0, 5) B(2, 3) C(– 4, 2) D(–1, –2)
Determine if the lines are parallel, perpendicular or neither.
1
y  2x  2
y  x2
41.
42.
2
y = 2x + 1
y = –2x + 4
43.
2x + y = 3
2x – 4y = 8
l
m
Use the picture at right to match each statement with its justification.
b
a
1 2
8 7
9 10
16 15
6
c
3 4
5
11 12
14 13
l
m
44. _____ if l m then 7  15
45. _____ 12  14
46. _____ if 3  11, then l m
A. Corresponding Angles Postulate
B. Alternate Interior Angle Theorem
C. Alternate Exterior Angle Theorem
47. _____ if a b then 11  15
D. Vertical angles are congruent.
48. _____ if l m then 5 and 12 are supplements
E. Same Side Interior Angle Theorem
49. _____ if a b and b c then a c
F. Converse of Alternate Exterior Angle Theorem
50. _____ if a b , then 1  5
G. Converse of Corresponding Angle Postulate
51. _____ if 4  14 , then l m
H. Converse of Same Side Interior Angle Theorem
52. _____ if m 6  m7  180 , then a b
I. If two lines are parallel to the same line, they are
parallel to each other.
Find the slope of the line containing the given points.
53.
(–2, 5) (6, 8)
54.
(4, 7) (4, 2)
55. (5, 1) (–2, 1)
Write the equation, in slope-intercept form, of the line meeting the following conditions.
56. slope = 2, passing through point (4, –5)
57. passing through the points (7, 4) and (5, 8)
58. passing through point (3, 1) parallel to y = –3x + 5
59. passing through point (8, –1) perpendicular to y = – 4x + 1
60. slope = – 4 and y-intercept = 5
61. slope = 0, passing through point (2, 5)