# Definition:Perpendicular Bisector

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## Definition

Let $AB$ be a line segment.

The **perpendicular bisector** of $AB$ is the straight line which:

- is perpendicular to $AB$

- passes through the point which bisects $AB$.

## Also known as

The **perpendicular bisector** of a line segment is also known as its **mediator**.

## Also see

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It follows from the parallel postulate that, in Euclidean geometry, the **perpendicular bisector** for any given line segment is unique.

- Results about
**perpendicular bisectors**can be found**here**.

## Sources

- 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**mediator** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**perpendicular bisector**