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 ==
''(awaiting image)''
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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 ABC to be collinear is that
 
<br><center><math>BD*CE*AF = -DC*EA*FB</math></center><br>
 
where all segments in the formula are [[directed segment]]s.
 
  
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<center><math>BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB</math></center>
  
== Example ==
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where all segments in the formula are [[directed segment]]s.
''Does anyone have a good example? ''
 
  
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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

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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 $D, E, F$ 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