how to do that (math)?

1. On each edge of a tetrahedron a point is fixed. Consider four tetrahedrons one of the vertices of each of which is a vertex of the initial tetrahedron and the remaining vertices are fixed points belonging to the edges that go out of this vertex. Prove that the volume of one of the tetrahedrons does not exceed 1/8 of the initial tetrahedron’s volume. 2. The opposite sides of a convex hexagon are pairwise parallel. Prove that the lines that connect the midpoints of opposite sides intersect at one point.