Alternate Interior Angles
From Latin: alternus "every other"
Alternate Interior Angles are created where a
transversal
crosses two (usually parallel) lines.
Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.
Try this Drag an orange dot at A or B. Notice that the two alternate interior angles shown are
equal in measure if the lines PQ and RS are parallel.
Referring to the figure above, the
transversal AB crosses the
two lines PQ
and RS
, creating intersections at E and F.
With each pair of alternate interior angles, both angles are inside the parallel lines and on opposite (alternate) sides of the transversal.
There are thus two pairs of these angles.
In the figure above, click on 'Other angle pair' to visit both pairs of alternate interior angles in turn.
Remember: interior means inside the parallel lines.
The parallel case
If the transversal
cuts across parallel lines (the usual case) then alternate interior angles have the same measure.
So in the figure above, as you move points A or B, the two alternate angles shown always have the same measure.
Try it and convince yourself this is true.
In the figure above, click on 'Other angle pair' to visit both pairs of alternate interior angles in turn.
The nonparallel case
If the transversal
cuts across lines that are not parallel, the alternate interior angles have no particular relationship to each other.
All we can say is that each angle is simply the alternate angle to the other.
Drag point P or Q to make the lines nonparallel. As you move A or B, you will see that the alternate interior
angles have no particular relationship to each other.
Other parallel topics
General
Angles associated with parallel lines
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