Perpendicular Bisector Theorem

Key Notes :

A point is equidistant from other points if it is the same distance from them.

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

X is on the perpendicular bisector of WY if and only if WX ≅ XY .

Definition:

The Perpendicular Bisector Theorem is a geometric principle that relates to a line segment and its perpendicular bisector.

Statement:

If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Key Concepts:

1. Perpendicular Bisector:
   • A line, segment, or ray that intersects another line segment at its midpoint and forms a right angle (90 degrees) with the segment.
2. Equidistant:
   • The distance from a point to each endpoint of a segment is equal.

Theorem Statement:

If a point P lies on the perpendicular bisector of segment AB, then PA=PB, where PA and PB are the distances from point P to the endpoints A and B respectively.

Example:

Consider line segment AB with midpoint M. If P is a point on the perpendicular bisector of AB, then PM=PA=PB.

Learn with an example

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