perpendicular bisector

(Mathematics - Euclidean Geometry)

The perpendicular bisector p of a line segment from A to B (A != B) is a line that is perpendicular to line AB and containing the midpoint of A and B. x is on p if and only if x is equidistant from A and B. The perpendicular bisectors of a triangle are also called side bisectors.

Also known as: side bisector (not noded).

The method for constructing a perpendicular bisector is detailed in Euclid's Elements, book I, proposition 10.

To construct the perpendicular bisector of a line AB with a compass and straight edge, follow these steps.

1. Put the compass point on A.
2. Open the compass to about 2/3 of the length AB.
3. Make one big arc from top to bottom which cuts through AB.
4. Put the compass point on B.
5. Make another big arc from top to bottom which cuts through AB.
6. You should now have two arcs that cut across AB, but also cross each other at two points, C and D.
7. Draw the line CD. It should be perpendicular to AB and bisect it.

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