Perpendicular bisector
In a plane, the perpendicular bisector of a line segment is a line
such that
and
are perpendicular and
passes through the midpoint of
.
In 3-D space, for each plane passing through there is a distinct perpendicular bisector. The set of lines which are perpendicular bisectors of form a plane which is the plane perpendicularly bisecting
.
In a triangle, the perpendicular bisectors of all three sides intersect at the circumcenter.