Geometry_Guided_Notes_Student_Copy_-Parallel-Lines-amp-TransversalsEdited.ppt

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1. Parallel Lines &
Transversals
Mrs. Wedgwood
Geometry

2. A
B
D
C
Parallel Lines and Transversals
What would you call two lines which do not intersect?
_____________
A solid arrow placed
on two lines of a
diagram indicate the
lines are parallel.
The symbol ____ is used to
indicate parallel lines.
AB ___ CD
Interior
Exterior
Exterior

3. Parallel Lines and Transversals
A slash through the parallel symbol || indicates the
lines are not parallel. ________________
A
D
B
C

4. Transversal
A _______, ______, or segment that intersects 2
or more ___________ lines, rays, or segments.
Parallel
lines
transversal
Non-Parallel
lines
transversal
Interior
Exterior
Exterior
Interior
Exterior
Exterior

5. Parallel Lines and Transversals
Transversal -
A __________ is a _______ which intersects
____ or _____ lines in a plane. The intersected
lines do not have to be parallel.
t
mk
j
Lines j, k, and m are
intersected by line t.
Therefore, line t is a
___________ of
lines j, k, and m.

6. interior
INTERIOR –The space ____________ the
2 lines
EXTERIOR -The space __________ the 2 lines
exterior
exterior

7. Special Angle Relationships
________________
<3 & <6 are ________ Interior angles
<4 & <5 are ________ Interior angles
<3 & <5 are _____ _____ Interior angles
<4 & <6 are _____ _____Interior angles
1
4
2
6
5
78
3
Exterior Angles
<1 & <8 are Alternate ________ angles
<2 & <7 are _________ Exterior angles
<1 & <7 are Same Side _______ angles
<2 & <8 are _____ ______ Exterior angles
Interior
Exterior
Exterior

8. Special Angle Relationships
WHEN THE LINES ARE
PARALLEL
♥Alternate Interior Angles
are ______________
♥Alternate Exterior Angles are
________________
♥Same Side Interior Angles are
________________
♥Same Side Exterior Angles are
_________________
1
4
2
65
78
3
If the lines are not
parallel, these angle
relationships DO
NOT EXIST.
Interior
Exterior
Exterior

9. Corresponding Angles &
Consecutive Angles
Corresponding Angles: Two ________ that occupy
______________ positions.
_________, _________, __________,
___________
12
34
56
78
Interior
Exterior
Exterior

10. Corresponding Angles
When two parallel lines are cut by a transversal, pairs of
corresponding angles are formed.
_____________of corresponding angles are formed.
Corresponding pairs of angles are _______________.




Line M
BA
Line N
D E
L
P
Q
G
F
Line L

11. Same Side
Interior/Exterior Angles
Same Side Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
Same Side Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
m3 +m5 = 180º, m4 +m6 = 180º
m1 +m7 = 180º, m2 +m8 =
180º
12
34
56
78
Interior
Exterior
Exterior

12. The angles that lie in the area between the two parallel lines
that are cut by a transversal, are called interior angles.
A pair of interior angles lie on the ______ ______of the
transversal.
Interior Angles
Line M
BA
Line N
D E
L
P
Q
G
F
Line L
60
0
120
0
120
0
60
0


Interior
Exterior
Exterior

13. 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.
__________________
__________________
12
34
56
78
Interior
Exterior
Exterior

14. Alternate Interior Angles
Alternate angles are formed on opposite sides of the
transversal and at different intersecting points.
Line M
BA
Line N
D E
L
P
Q
G
F
Line L


Pairs of alternate angles are _____________.
___________of alternate angles are formed.

15. Let’s Practice
m<1=_________°
Find all the remaining
angle measures.
1
4
2
65
78
3
120

16. Another practice problem
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.
40
120

17. Name the pairs of the following angles formed by a
transversal.