The angle bisector of angle BAC is a ray AD such that AD is between AB and AC and the measure of angle BAD = the measure of angle DAC. The distance from a point to a line is measured along a perpendicular.
Prove the following theorem. Pointwise Characterization of Angle Bisector. A point P lies on the bisector of angle BAC if and only if P is in the interior of angle BAC and the distance from P to AB equals the distance from P to AC.