Question

Given two parallelograms: `ABCD` and `A^'B^'C^'D^'`. Let `A^″ ` be the midpoint of the segment `A\A^'`, `B^″ ` be the midpoint of the segment `B\B^'`, and so on. Prove that `A^″B^″ C^″ D^″ ` is a parallelogram.