Tetrahedron!!!!! help!?

Question

Prove that the lines joining the midpoints of the opposite edges of a tetrahedron
intersect and bisect each other.

Answer 1

Let a, b, c, d be 4 vectors representing the vertices of an arbitrary tetrahedron. Then the midpoints of the edges would be of the form (1/2)(x+y), where x and y are any a, b, c, d, making for 6 midpoints. Then the midpoint of the vector connecting any pair of midpoints will have the form: (1/4)(a+b+c+d), regardless of which opposite pairs are selected. QED.