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Congruent Angles
Definition: Angles are congruent if they have the same angle measure in degrees.
Try this Adjust any angle below by dragging an orange dot at its ends. The other angle will change to remain congruent with it.
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Angles are congruent if they have the same angle measure in degrees. They can be at any orientation on the plane. In the figure above, there are two congruent angles. Note they are pointing in different directions. If you drag any of the endpoints, the other angle will change to remain congruent with the one you are changing.

For angles, 'congruent' is similar to saying 'equals'. You could say "the measure of angle A is equal to the measure of angle B". But in geometry, the correct way to say it is "angles A and B are congruent".

To be congruent the only requirement is that the angle measure be the same, the length of the two arms making up the angle is irrelevant. As you drag the orange dots above, note how the line lengths will vary but the angles remain congruent, because only the angle measure in degrees matters..

Symbols

The symbol for congruence is congruence

Also recall that the symbol for an angle is , so the statement

ABC PQR
is read as "The angle ABC is congruent to the angle PQR".

Constructing congruent angles

It is possible to construct (draw) an angle that is congruent to a given angle with a compass and straightedge. For more on this see Copying an angle.
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Other congruence topics

Congruent Triangles

Congruent Polygons