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 non-parallel 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 non-parallel. 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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