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,