Difference between revisions of "Perpendicular bisector"

 
m
Line 1: Line 1:
A '''perpendicular bisector''' of a [[line segment]] <math>AB</math> is a line segment <math>CD</math> such that <math>AB</math> and <math>CD</math> are perpendicular and <math>CD</math> divides <math>AB</math> into two equal segments.
+
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 08:48, 18 August 2006

In a plane, the perpendicular bisector of a line segment $AB$ is a line $l$ such that $AB$ and $l$ are perpendicular and $l$ passes through the midpoint of $AB$.

In 3-D space, for each plane passing through $AB$ there is a distinct perpendicular bisector. The set of lines which are perpendicular bisectors of form a plane which is the plane perpendicularly bisecting $AB$.

In a triangle, the perpendicular bisectors of all three sides intersect at the circumcenter.