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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.
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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
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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
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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
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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
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To Try Some Practice Problems
Involving These Relationships
CLICK HERE
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