Difference between revisions of "Perpendicular bisector"
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| − | + | 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>. | |
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| + | 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.
