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ABCD is a tetrahedron (not necessarly a regular one). A Monge's plane is a plane which is perpendicular to an edge and goes through the middle of the opposite edge.

Monge's plan

I want to prove that the 6 Monge's planes of this triangle converge in a unique point and I haven't got any idea of the way to do this.

Thank you in advance !

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    You've tried taking the coordinate geometry route?2011-10-26
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    I tried but there are too many unknowns and I don't see how to characterize this kind of conditions.2011-10-26
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    The strategy I had in mind was for you to take three of those planes, find their intersection, and then verify that that point lies in those three other planes...2011-10-26
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    Okay, this might help you with simplifying things: position your tetrahedron such that one vertex is at the origin and one of the edges lies on an axis. Have one of the faces lie in a coordinate plane, if needed. You might want to use the formulae [here](http://mathworld.wolfram.com/Plane.html) to help you with assembling plane equations.2011-10-26

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Here's a concise linear algebra proof (pages 5 and 6). And here's a geometrical proof.

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    I'm watching this tonight but your second link seems dead...2011-10-26
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    Sorry, I grabbed a redirected link that contained a session code. Fixed. By the way, you're *looking at* this tonight. "Watching" is for observing something that may change over time, like a process or a movie or a game or a sunset.2011-10-26
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    Oh, I didn't know :) I'm not english ! Thank you.2011-10-26