# PERPENDICULAR BISECTOR THEOREM

Perpendicular Bisector Theorem :

In this section, we are going to study one of the important theorems in mathematics — Perpendicular Bisector Theorem.

## Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

## Perpendicular Bisector Theorem Proof

Given :

P is the perpendicular bisector L of segment AB and M is the intersection of AB and line L.

To Prove :

PA  ≅  PB

Proof :

 Statement AB  ≅  MB∠AMP  ≅  ∠BMPPM  ≅  PMΔAMP  ≅  ΔBMPPB  ≅  PB ReasonDefinition of perpendicular bisectors Both angles measure 90°Reflexive propertySAS congruence postulateCorresponding parts of congruent triangles are congruent.

After having gone through the stuff given above, we hope that the students would have understood, "Perpendicular Bisector Theorem".

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