The Perpendicular Bisector Theorem | Understanding the Relationship between Equidistant Points and the Bisector of a Segment

Perpendicular Bisector Theorem

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

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

Let’s break down what this means. Imagine you have a line segment AB. The perpendicular bisector of AB is a line that passes through the midpoint of AB and is perpendicular to it, dividing it into two equal halves.

According to the Perpendicular Bisector Theorem, if you have a point C that is equidistant from A and B, then point C will lie on the perpendicular bisector of AB. In other words, the distance from C to A will be the same as the distance from C to B.

This theorem can be particularly useful in geometry problems or constructions. It allows us to find points on the perpendicular bisector of a segment by simply locating points that are equidistant from the endpoints of the segment.

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

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