3.3.42 (Perpendicular bisectors concurrence proof)
Prove that the perpendicular bisectors of the sides of a triangle are concurrent.
Consider the triangle . Let the perpendicular bisectors of the sides and intersect at point O.
Because and , we have . Now consider the point F that bisects the segment . Because it is a bisector, we know that . We also know that is congruent to itself. Thus, by the SSS criterion for congruence, .