Difference between revisions of "Menelaus' Theorem"

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#REDIRECT[[Menelaus' theorem]]
 
 
'''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 <math>D, E, F</math> on the respective side lines <math>BC, CA, AB</math> of a triangle <math>ABC</math> to be collinear is that
 
 
 
<center><math>BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB</math></center>
 
 
 
where all segments in the formula are [[directed segment]]s.
 
 
 
[[Image:Menelaus1.PNG|center]]
 
 
 
== See also ==
 
* [[Ceva's Theorem]]
 
* [[Stewart's Theorem]]
 

Latest revision as of 16:20, 9 May 2021

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