Tetra Slice

$ABCD$ is a tetrahedron.  

Points $P$, $Q$, $R$ and $S$ are the midpoints of sides $AB$, $BD$, $CD$ and $AC$.

Prove that $PQRS$ is a parallelogram.

Extension

If $ABCD$ is a regular tetrahedron, what else can you say about $PQRS$?