Difference between revisions of "Menelaus' Theorem"
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| + | '''Menelaus' Theorem''' deals with the [[collinearity]] of points on each of the three sides (extended when necessary) of a [[triangle]]. | ||
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== Statement == | == 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 | |
| − | A necessary and sufficient condition for points D, E, F on the respective side lines BC, CA, AB of a triangle | ||
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| − | |||
| + | <center><math>BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB</math></center> | ||
| − | + | where all segments in the formula are [[directed segment]]s. | |
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| + | [[Image:Menelaus1.PNG|center]] | ||
== See also == | == See also == | ||
* [[Ceva's Theorem]] | * [[Ceva's Theorem]] | ||
* [[Stewart's Theorem]] | * [[Stewart's Theorem]] | ||
Revision as of 23:53, 18 August 2006
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.
Statement
A necessary and sufficient condition for points 
on the respective side lines 
of a triangle 
to be collinear is that
where all segments in the formula are directed segments.
