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Parallel Lines &
Transversals
Mrs. Wedgwood
Geometry
Parallel Lines and Transversals
What would you call two lines which do not intersect?
_____________
Exterior
B
A
Interior
D
A solid arrow placed
on two lines of a
diagram indicate the
lines are parallel.
C
Exterior
The symbol ____ is used to
indicate parallel lines.
AB ___ CD
Parallel Lines and Transversals
A slash through the parallel symbol || indicates the
lines are not parallel. ________________
B
A
D
C
Transversal
A _______, ______, or segment that intersects 2
or more ___________ lines, rays, or segments.
Exterior
Exterior
Parallel
lines
Interior
Non-Parallel
lines
Interior
Exterior
Exterior
transversal
transversal
Parallel Lines and Transversals
Transversal A __________ is a _______ which intersects
____ or _____ lines in a plane. The
intersected lines do not have to be parallel.
j
k
m
t
Lines j, k, and m are
intersected by line t.
Therefore, line t is a
___________ of
lines j, k, and m.
INTERIOR
–The space ____________ the
2 lines
interior
EXTERIOR
-The space __________ the 2 lines
exterior
exterior
Special Angle Relationships
________________
Exterior
1
3 4
Interior
5 6
7 8
Exterior
2
<3 & <6 are ________ Interior angles
<4 & <5 are ________ Interior angles
<3 & <5 are _____ _____ Interior angles
<4 & <6 are _____ _____Interior angles
Exterior Angles
<1 & <8 are Alternate ________ angles
<2 & <7 are _________ Exterior angles
<1 & <7 are Same Side _______ angles
<2 & <8 are _____ ______ Exterior angles
Special Angle Relationships
WHEN THE LINES ARE
PARALLEL
♥Alternate Interior Angles
Exterior
1
2
3 4
Interior
5 6
7 8
Exterior
If the lines are not
parallel, these angle
relationships DO
NOT EXIST.
are ______________
♥Alternate Exterior Angles are
________________
♥Same Side Interior Angles are
________________
♥Same Side Exterior Angles are
_________________
Corresponding Angles &
Consecutive Angles
Corresponding Angles: Two ________ that occupy
______________ positions.
_________, _________, __________,
___________
Exterior
1
3
5 6
7 8
2
4
Interior
Exterior
Corresponding Angles
When two parallel lines are cut by a transversal, pairs of
corresponding angles are formed.
L
Line L
______________
G
P
A
D
B
Q
E
F
Line M
Line N
_____________
_____________
_____________
_____________of corresponding angles are formed.
Corresponding pairs of angles are _______________.
Same Side
Interior/Exterior Angles
Same Side Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º
Same Side Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
Exterior
1 2
m1 +m7 = 180º, m2 +m8 = 180º
3 4
Interior
5 6
7 8
Exterior
Interior Angles
The angles that lie in the area between the two parallel lines
that are cut by a transversal, are called interior angles.
L
G
Line L
Exterior
A 1200 P
1200
600
D
B
600
F
________________
Line N
_________________
Interior
E
Q
Line M
Exterior
A pair of interior angles lie on the ______ ______of the
transversal.
Alternate Interior/Exterior Angles
• __________________: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
__________________
____________________: Two angles that lie outside parallel
lines on opposite sides of the transversal.
__________________
1 2 Exterior
3 4
Interior
5
7
6
8
Exterior
Alternate Interior Angles
Alternate angles are formed on opposite sides of the
transversal and at different intersecting points.
L
G
A
D
Line L
P
B
Q
E
Line M
Line N
____________
____________
F
___________of alternate angles are formed.
Pairs of alternate angles are _____________.
Let’s Practice
120 1
3
7
4
6
5
8
2
m<1=_________°
Find all the remaining
angle measures.
Another practice problem
40
120
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.
Name the pairs of the following angles formed by a
transversal.