Difference between revisions of "Menelaus' Theorem"

m
Line 15: Line 15:
 
* [[Ceva's Theorem]]
 
* [[Ceva's Theorem]]
 
* [[Stewart's Theorem]]
 
* [[Stewart's Theorem]]
 +
 +
[[Category:Theorems]]
 +
 +
[[Category:Geometry]]

Revision as of 20:35, 14 October 2007

This article is a stub. Help us out by expanding it.

Menelaus' Theorem deals with the collinearity of points on each of the three sides (extended when necessary) of a triangle. It is named for Menelaus of Alexandria.

Statement

A necessary and sufficient condition for points $D, E, F$ on the respective side lines $BC, CA, AB$ of a triangle $ABC$ to be collinear is that

$BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB$

where all segments in the formula are directed segments.

Menelaus1.PNG

See also