Theorem:

he Midpoint Theorem: ( The Definition of Midpoint)

Given AB, its midpoint M is:
2AM = AB and AM = ½ AB
2MB = AB and MB = ½ AB

A perpendicular bisector of a segment is a line, ray or another segment that is perpendicular to the segment at its midpoint.

Theorem:

f a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

Theorem:

f a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.