Intersection of a Plane and a Tetrahedron
Let be a tetrahedron and let and be the midpoints of the edges and . Let a plane that contains the line intersect the edges and at points and . Then bisects .
A proof is described in [1, p. 126].
 V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.