In a given tedrahedron

let

and

be the centres of edges

and

respectively. Prove that every plane that contains the line

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.