Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
Practice Form G
Properties of Parallel Lines
Identify all the numbered angles that are congruent to the given angle. Justify
your answers.
1. 2.
3.
4.
Find
mj1
and
mj2
. Justify each answer.
5. 6.
7.
8.
Algebra Find the value of x and y. en nd the measure of each
labeled angle.
9. 10.
11. 12.
132
1
2
3
4
5
6
7
1 2
4
78
5
6
8
7
1
2
3
4
5
6
7
88
1
2
3
4
5
67
b
q
r
1
2
130
z
e
d
1
2
79
Q
R
S
T
1
2
76
119
a
b
2
58
82
1
s
t
(
x
26)
x
x
2
(7
x
)°
°
(
x
55)
(3
x
5)
(
x
20)
(
x
10)
(
y
40)
y
j3
; vert.
⦞
are
@
;
j5
; corresp.
⦞
are
@
;
j7
; alt. ext.
⦞
are
@
.
j1
; vert.
⦞
are
@
;
j5
; alt. int.
⦞
are
@
;
j7
; corresp.
⦞
are
@
.
j5
; vert.
⦞
are
@
;
j3
;
corresp.
⦞
are
@
;
j1
;
alt. ext.
⦞
are
@
.
j4
; vert.
⦞
are
@
;
j2
; alt. int.
⦞
are
@
.
mj1 = 50
;
⦞
that
form a linear pair
are suppl.;
mj2 = 130
;
corresp.
⦞
are
@
.
mj1 = 79
; alt.
ext.
⦞
are
@
;
mj2 = 101
;
⦞
that form a linear
pair are suppl.
mj1 = 76
; alt.
int.
⦞
are
@
;
mj2 = 61
;
same-side int.
⦞
are suppl.
mj1 = 82
;
corresp.
⦞
are
@
;
mj2 = 122
;
the
58°
j
and
the
j
below
j2
are alt. int.
⦞
and are
@
.
Because
j2
and
the
j
below it
form a linear
pair, they are
suppl.
103; 77;
103°
24; 12; 168
30; 85; 85
75; 95; 85; 70; 110
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
Practice (continued) Form G
Properties of Parallel Lines
13. Write a two-column proof.
Given: a
}
b, x
}
y
Prove:
∠4
is supplementary to
∠15
.
Statements Reasons
14. Visualization One pair of parallel lines intersect a second pair of parallel
lines. One of the angles of intersection has a measure of 60. How can you
determine the measure of the four interior angles? Draw a sketch to support
your answer.
15. Error Analysis Which solution for the gure at the
right is incorrect? Explain.
2x - 40 = x + 10
2x - 40 + (x + 10) = 180
x - 40 = 10
3x - 30 = 180
x = 50
3x = 210
x = 70
16. A zip line consists of a pulley attached to a cable
that is strung at an angle between two objects.
In the zip line at the right, one end of the cable
is attached to a tree. e other end is attached
to a post parallel to the tree. What is the measure
of
∠1
? What type of angle pair do
∠1
and the
given angle represent?
a
b
x y
1 2
3
4
5 6
7
8
9
10
11
12
13
14
15
16
q r
e
f
(2
x
40)
(
x
10)
1
115
1)
x } y
;
a } b
2)
j15 @ j9
3)
mj15 = mj9
4)
j9
and
j4
are suppl.
5)
mj9 + mj4 = 180
6)
mj15 + mj4 = 180
7)
j15
and
j4
are suppl.
1) Given
2) Alt. ext. angles are
@
.
3) Definition of congruent
4) Same-side int.
⦞
are suppl.
5) Def. of suppl.
⦞
6) Substitution property
7) Def. of suppl.
⦞
Answers may vary. Sample:
Answers may vary. Sample: If the measure of the
given angle is 60, then
mjA
and
mjC
are both 120 because
same-side interior angles are supplementary. Because
jC
and
jD
are also supplementary,
mjD
is 60.
Second solution; the angles are alternate
interior angles, which means they are
congruent.
A
C
D
60
115°
; alternate interior angles
