Understanding the Perpendicular Bisector Theorem | Explained and Applied for Geometry

Converse of the Perpendicular Bisector Theorem

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

The converse of the Perpendicular Bisector Theorem is a statement that can be derived from the original theorem. It states that if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

In simpler terms, if a point P is the same distance from points A and B, then the line containing point P is the perpendicular bisector of segment AB.

This converse is useful in geometry because it allows us to determine the position of a line by considering the distances between points. We can apply this theorem to find the equation of the perpendicular bisector of a segment, or to prove that a line is the perpendicular bisector of a segment.

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