Corresponding Angles
From Latin: co "together" + respondere "answer to"
Corresponding angles are created where a
transversal
crosses other (usually parallel) lines.
The corresponding angles are the ones at the same location at each
intersection.
Try this Drag an orange dot at A or B. Notice that the two corresponding 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. If the two lines are parallel, the four angles around E are the same
as the four angles around F. This creates four pairs of corresponding angles.
In the figure above, click on 'Next angle pair' to visit each pair in turn.
The parallel case
If the transversal
cuts across parallel lines (the usual case) then corresponding angles have the same measure.
So in the figure above, as you move points A or B, the two corresponding angles always have the same measure.
Try it and convince yourself this is true. C
In the figure above, click on 'Next angle pair' to visit all four sets of corresponding angles in turn.
The nonparallel case
If the transversal
cuts across lines that are not parallel, the corresponding angles have no particular relationship to each other.
All we can say is that each angle is simply the corresponding 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 corresponding
angles have no particular relationship to each other.
Other parallel topics
General
Angles associated with parallel lines
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