Why Is the Perpendicular Bisector Theorem?

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn. If a pillar is standing at the center of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge.

What is the theorem of perpendicular bisector?

Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

Why is the perpendicular bisector theorem important?

Perpendicular bisector theorem deals with congruent segments of a triangle, thus allowing for the diagonals from the vertices to the circumcenter to be congruent. Whereas the angle bisector theorem deals with congruent angles, hence creating equal distances from the incenter to the side of the triangle.