Angles Formed by Parallel Lines
Cut by a Transversal: Lesson

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In this lesson we will be discovering some very special relationships between the angles that are formed when a pair of parallel lines are cut by a transversal.
In the diagram below you can see that lines AB and CD are parallel
and that the third line, EF is a transversal.
When this occurs you can also see that 8 different angles
have been created...which have been numbered 1 - 8

It turns out that each of these angles can be paired with another,
and that each pair of angles has a special name,
as well as a special property.

 


Corresponding Angles
In the diagram above, the following pairs of angles
are called corresponding angles:
<1 and <5
<2 and <6
<3 and <7
<4 and <8
If you look at where each of the angles in a pair are located,
you will notice that they are in the same relative position
where the transversal intersects one of the parallel lines
and the same point of intersection on the other parallel line.
In other words, the position of one of the angles corresponds
to the position of the other angle in the pair.

As for their special property....
Corresponding angles are equal.
<1 = <5
<2 = <6
<3 = <7
<4 = <8
 

 


Alternate Interior Angles
In the diagram above, angles 3,4,5 and 6 are
called interior angles because they are between the two parallel lines. If the angles lie on opposite sides of the transversal, but not on the same parallel line,
they are called alternate interior angles.
The pairs of alternate interior angles in this diagram are:
<3 and <6
<4 and <5

As for their special property:

Alternate Interior angles are equal.
<3 = <6
<4 = <5
 

 


Alternate Exterior Angles
In the diagram above, angles 1,2,7 and 8 are called exterior angles because they do not lie between the parallel lines.
Just like alternate interior angles, if the exterior angles lie on opposite sides of the transversal, but not at the same parallel line, they are called alternate exterior angles.
The pairs of alternate exterior angles in the diagram are:
<1 and <8
<2 and <7

The special property of these angle pairs:
Alternate Exterior angles are equal.
<1 = <8
<2 = <7
 

 


Interior Angles on the Same Side of the Transversal
As the name clearly implies, the diagram above shows that :
<3 and <5
<4 and <6
are pairs of angles which are not only interior angles,
but also lie on the same side of the transversal.

The special property of these angle pairs:
Interior Angles on the Same Side of the Transversal
are
SUPPLEMENTARY
(THEIR SUM IS ALWAYS 1800)
<3 + <5 = 1800
<4 + <6 = 1800
 

To Try Some Practice Problems
Involving These Relationships

CLICK HERE

 
Topic Index | Grade 8 Math | Intermediate Test Prep | StudyZone

Created by Paul DeRitter
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