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PROPERTIES
OF
PARALLEL
LINES
Transversal
Line that intersect two coplanar lines at two
distinct points
Eight angles are formed by a transversal line
5 6
1 3
4 2
7 8
Alternate interior angles
Angles inside the two lines on opposite sides of the
transversal
<3 and < 4
<1 and <2
1 3
4 2
Same side interior angles
Angles inside the two lines on the same side of the
transversal
< 1 and < 4
< 2 and < 3
1 3
4 2
Corresponding angles
Angles that are in similar positions on the same side of
a transversal
<2 and <6
<5 and < 4
5 6
1 3
<1 and <7
<3 and <8
4 2
7 8
When a transversal intersect two PARALLEL lines,
then corresponding angles are congruent in other
words they have the same angle measure
The two small red arrows indicate the two lines are
parallel
5 6
1 3
4 2
7 8
When a transversal intersect two PARALLEL lines
the alternate interior angles are congruent
In this example < 1 and < 2
<3 and < 4
1 3
4 2
When a transversal intersects two PARALLEL lines,
then the same-side interior angles are supplementary
This is saying
m < 1 + m < 4 = 180
Likewise m < 2 + m < 3 = 180
1 3
4 2
What are some things we can state from this diagram?
Parallel lines
Alternate interior angles
Corresponding angles
Same side interior angles
5 6
1 3
Vertical
angles
l
m
4 2
7 8
If <6 and < 2 are
corresponding then <1
and <6 are vertical so
<1 and < 2 would also
have the same measure
Find the measure of each angle:
c
a
b
d
8 7
6
500
5
2
1
4
3
Find the values of x and y
x=
Corresponding angles of parallel lines are congruent
y=
70 + 50 + y = 180
500
x
y
700
Find the values of x and y. Then find the measure of
the angles
Same side interior angles = 180
90 + 2x = 180
x = 45
y + y – 50 = 180
2y – 50 = 180
90
2x
y
115
2y = 230
y = 115
(y – 500)
90
65
ASSIGNMENT
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