This document discusses perpendicular bisectors and their properties. It defines a perpendicular bisector as a line that is perpendicular to a segment at its midpoint and is equidistant from the segment's endpoints. It presents the theorem that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. It also presents the converse theorem - that if a point is equidistant from the endpoints, then it lies on the perpendicular bisector. Examples and proofs of these theorems are provided.