Parallel And Perpendicular Lines Worksheet Page 28
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50Proving Lines Parallel
•
Recognize angle conditions that occur with parallel lines.
•
Prove that two lines are parallel based on given angle relationships.
do you know that the sides of
do you know that the sides of
a parking space are parallel?
a parking space are parallel?
Have you ever been in a tall building and
looked down at a parking lot? The parking
lot is full of line segments that appear to be
parallel. The workers who paint these lines
must be certain that they are parallel.
IDENTIFY PARALLEL LINES
When each stripe of a parking space intersects
the center line, the angles formed are corresponding angles. If the lines are parallel,
we know that the corresponding angles are congruent. Conversely, if the
corresponding angles are congruent, then the lines must be parallel.
Postulate 3.4
Postulate 3.4
If two lines in a plane are cut by a transversal so that
m
corresponding angles are congruent, then the lines
1
2
are parallel.
3
4
If corr.
are
, then lines are
Abbreviation:
.
n
5
6
If
1
5,
2
6,
3
7,
Examples:
7
8
or
4
8, then m n.
Postulate 3.4 justifies the construction of parallel lines.
Parallel Line Through a Point Not on Line
Use a straightedge to
Copy
PMN so that
Draw PQ. Because
2
2
3
1
1
3
draw a line. Label two
P is the vertex of the
RPQ
PMN by
Study Tip
points on the line as
new angle. Label the
construction and they
Look Back
M and N. Draw a
intersection points
are corresponding
To review copying angles,
point P that is not
Q and R.
angles, PQ MN.
see Lesson 1-4.
on MN. Draw PM.
Lesson 3-5 Proving Lines Parallel 151
David Sailors/CORBIS
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