Proof of Concurrence of the Perpendicular Bisectors of
a Triangle.

By Colleen Garrett

Given: Triangle ABC. Claim: The perpendicular
bisectors of Triangle ABC concur at point P. Construct the perpendicular
bisectors of two sides of the triangle.

Construct PB and PA and
PC. Point P is equidistant from
points A and B because points lying on the perpendicular bisector are
equidistant from the segments endpoints. Hence PBPA. Similarly, PCPA.

By transitivity, PCPB therefore, P is equidistant from points B and C. P then lies on the perpendicular
bisector of segment BC. Hence, the
perpendicular bisectors of a triangle concur at point P.