- **Geometry**
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- - **Geometry Proof**
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Geometry ProofThe perpendicular bisector of a segment AB is a line l such that l intersects AB at its midpoint and l is perpendicular to AB. Prove the following theorem:Pointwise Characterization of Perpendicular Bisector. A point P lies on the perpendicular bisector of AB if and only if PA = PB. |

Re: Geometry ProofI think the proof is very simple, if you know some fundamental theorems of geometry. |

Re: Geometry ProofA point on the perpendicular bisector connected to the end points gives a figure consisting of two right triangles with the legs equal. Therefore the hypotenuses are equal. For a point (P) off the bisector, compare to the point (Q) on the bisector at the same distance from the line. Assume P is on the A side of the bisector, the |PA| < |QA| and |PB| > |QB|. Meanwhile |QA| = |QB|. All these statements follow from the pythagorean theorem. |

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