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 julian21 September 3rd, 2010 11:16 AM

Geometry Proof

The 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.

 thomasthomas September 3rd, 2010 12:17 PM

Re: Geometry Proof

I think the proof is very simple, if you know some fundamental theorems of geometry.

 mathman September 3rd, 2010 02:05 PM

Re: Geometry Proof

A 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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