Definition:Perpendicular Bisector

Definition
Let $AB$ be a line segment.

The perpendicular bisector of $AB$ is the straight line which:


 * is perpendicular to $AB$


 * passes through the point which bisects $AB$.


 * PerpendicularBisector.png

Also see

 * Perpendicular Bisector is Locus of Points Equidistant from Endpoints

It follows from the parallel postulate that, in Euclidean geometry, the perpendicular bisector for any given line segment is unique.