PERPENDICULAR BISECTOR THEOREM

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

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 ≅ ∠BMP

PM ≅ PM

ΔAMP ≅ ΔBMP

PB ≅ PB

Reason

Definition of perpendicular bisectors

Both angles measure 90°

Reflexive property

SAS congruence postulate

Corresponding parts of congruent triangles are congruent.

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