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 that segment.

PROOF

Statement         Reason FD is the perpendicular bisector of AD  Given Af = Bf         Definition of perpendicular bisector (cuts segment in half) <AFD=<BFD       Definition of perpendicular bisector(angles are the same 90) Df=Df         Reflexive triangle BDF=triangle ADF    SAS AD=DB        CpCTC