In the figure, the ray bisects the angle .
The angles and are congruent.
Note that any point on the angle bisector is equidistant from the two sides of the angle. Some textbooks call this Angle Bisector Theorem , but this name is usually used for another theorem about angle bisectors in a triangle.
In the figure, is an angle bisector. Find the measure of .
Since is an angle bisector,
By the Angle Addition Postulate,