# perpendicular

Construction of a perpendicular.

To be perpendicular is to be at right angles. Two lines, planes, etc., are said to be perpendicular if they are 90° apart.

## Perpendicular bisector

The **perpendicular bisector of a given line segment** *AB* is the straight line perpendicular to *AB*, and passing through its mid-point. The **perpendicular bisector of a segment** is the axis of symmetry of the segment. The **perpendicular bisectors of the three sides of a triangle** intersect in the center of the circumcircle.

## Construction of a perpendicular

To drop a perpendicular onto a straight line.

*Construction*: Given a straight line *l* and a point *P* outside the line. Describe a circle (of arbitrary radius) about *P* so that it intersects *l* in two points *A* and *B*. About *A* and *B* draw circles large enough to intersect and join their points of intersection, *C* and *D*. The required perpendicular lies on the line through *C* and *D*, and is the join of *P* to the point *F* where *L* and *CD* intersect.