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 00:53, 19 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
![$BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB$](http://latex.artofproblemsolving.com/0/4/5/045a215225c903c05bd169d618043067ce17cd8d.png)
where all segments in the formula are directed segments.