Parallel Line Theorems

1
Parallel
Line
Theorems
2
Parallel lines are like train tracks.They never
cross.
3
Parallel Line Theorems

• Two parallel lines on their own are not vary
  interesting to us in terms of geometry.
• But if straight line (called a transversal)
  intersects two parallel lines, then the angles
  created are very interesting to us..

4
These lines are parallel because they will never
cross.
The dashed line is called a transversal, because
it crosses both lines
5
As soon as the transversal is drawn, a collection
of angles are created. These angles are equal
because of OAT. Copy these to your sheet.
x
y
y
x
x
y

• x

y
In this diagram, there is a collection of
patterns that can be generated.
6
y
y
Z pattern (alternate angles AA)
7
x
x
Z pattern
8
y
x
y

• x

F pattern (corresponding angles CA)
9
x
y
x
y
F pattern
10
y
x
X Y 180O
x
y
C pattern (supplementary angles SA)
( also called interior angles )
11
Find X,Y and Z
Statement Reason

• 70O

Z
Z 70O
OAT
Y 180O 70O
SA
110O
Y
X
X 110O
OAT
12
HOMEWORKsee sheet