Pointwise Characterization of Perpendicular Bisector Proof

The perpendicular bisector of a segment AB is a line l such that l intersects AB at its midpoint and l is perpendicular to AB. Prove the following theorem:

Pointwise Characterization of Perpendicular Bisector. A point P lies on the perpendicular bisector of AB if and only if PA = PB.

Prove two congruent triangles by SAS: Perpendicular, Bisector, Reflexive property, Creates Isosceles Triangle by CPCTC.