If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
P is on the perpendicular bisector l of segment AB.
What To Show
Let be the intersection of and line .
. Definition of perpendicular bisector. (S)
Both angles measure (definition of perpendicular bisector). (A)
. A segment is congruent to itself (Reflexive property, Axiom E1). (S)
By SAS Congruence, triangle is congruent to triangle .
Now, and are corresponding sides of triangles and .
Since corresponding parts of congruent triangles are congruent, . This completes the proof.