Difference between revisions of "Perpendicular bisector"
m |
|||
Line 1: | Line 1: | ||
− | + | In a [[plane]], the '''perpendicular bisector''' of a [[line segment]] <math>AB</math> is a [[line]] <math>l</math> such that <math>AB</math> and <math>l</math> are [[perpendicular]] and <math>l</math> passes through the [[midpoint]] of <math>AB</math>. | |
+ | |||
+ | In 3-D space, for each plane passing through <math>AB</math> there is a distinct perpendicular bisector. The [[set]] of lines which are perpendicular bisectors of form a plane which is the plane perpendicularly bisecting <math>AB</math>. | ||
In a [[triangle]], the perpendicular bisectors of all three sides intersect at the [[circumcenter]]. | In a [[triangle]], the perpendicular bisectors of all three sides intersect at the [[circumcenter]]. | ||
[[Category:Definition]] | [[Category:Definition]] |
Revision as of 09:48, 18 August 2006
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.