In a given tedrahedron
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
let
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
and
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
be the centres of edges
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
and
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
respectively. Prove that every plane that contains the line
![KL](/media/m/b/1/a/b1ab64b407588444cd365224f9b482b4.png)
divides the tedrahedron into two parts of equal volume.
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In a given tedrahedron $ABCD$ let $K$ and $L$ be the centres of edges $AB$ and $CD$ respectively. Prove that every plane that contains the line $KL$ divides the tedrahedron into two parts of equal volume.