A
transversal is a line that intersects two or more
lines (in the same plane). When lines intersect, angles
are formed in several locations. Certain angles are given
"names" that describe "where" the angles are located in relation
to the lines. These names describe
angles whether the lines involved are parallel or not parallel.
Remember that:
 the word
INTERIOR means
BETWEEN the lines.
 the word
EXTERIOR means
OUTSIDE the
lines.
 the word
ALTERNATE means
"alternating sides" of the transversal.
When the lines are NOT
parallel ... 
When the lines are
parallel... 



The names "alternate interior angles",
"alternate exterior angles", "corresponding angles", and "interior angles on
the same side of the transversal" are used to describe specific angles
formed when lines intersect. These names are used both when lines are parallel and when
lines are not parallel.
Let's examine these angles, and
other angles, when the lines are parallel. 
When the lines are
parallel:
Alternate Interior
Angles
(measures
are equal)
The name clearly describes "where"
these angles are located. 
Look carefully at the diagram
below: 

Hint: If you
draw a Z on the diagram, the alternate interior angles
are found in the corners of the Z. The Z may also be a backward Z.

If two parallel lines are cut by
a transversal, the alternate interior angles are
congruent. 


If two lines are cut by a
transversal and the alternate interior angles are
congruent, the lines are parallel. 

When the lines are
parallel:
Alternate Exterior
Angles
(measures
are equal)
The name clearly describes "where"
these angles are located. 
Look carefully at the diagram
below:



If two parallel lines are cut by
a transversal, the alternate exterior angles are
congruent. 


If two lines are cut by a
transversal and the alternate exterior angles are
congruent, the lines are parallel. 

When the lines are
parallel:
Corresponding Angles
(measures
are equal)
Unfortunately, the name of these
angles
does not clearly indicate "where" they
are located. They are located:
 on the SAME SIDE of the transversal
 one INTERIOR and one EXTERIOR
 and they are NOT adjacent (they don't touch).
(They lie on the same side of the
transversal,
in corresponding positions.) 


Hint: If you
took a picture of one corresponding angle and slid
the angle up (or down) the same side of the transversal, you
would arrive at the other corresponding angle.
Also: If you
draw an F on the diagram, the corresponding angles can be
found in the "corners" of the F. The F may be backward and/or
upsidedown.

If two parallel lines are cut by
a transversal, the corresponding angles are
congruent. 


If two lines are cut by a
transversal and the corresponding angles are
congruent, the lines are parallel. 

When the lines are
parallel:
Interior Angles on the
Same Side of the Transversal
(measures
are supplementary)
Their "name" is simply a
description of where the angles are located.




If two parallel lines are cut by
a transversal, the interior angles on the same side
of the transversal are supplementary. 


If two lines are cut by a
transversal and the interior angles on the same side
of the transversal are supplementary, the lines are
parallel. 

Of course, there are also other angle
relationships occurring when working with parallel lines.
Vertical Angles
(measures
are equal)
Vertical angles are ALWAYS equal, whether you
have parallel
lines or not. 
Refresh your memory using the diagram below: 


Vertical angles are congruent. 

Angles forming a Linear
Pair
(Adjacent Angles creating
a Straight Line)
(measures
are supplementary) 
This is an
"old" idea about angles revisited. Since a
straight angle contains 180°, these two adjacent angles
add to 180. They form a linear pair.
(Adjacent angles share a vertex, share a side, and do not
overlap.) 


If two angles form a linear pair,
they are supplementary. 

