Answer
The inner parallelogram creates four separate triangles. We must prove that the triangles opposite each other a congruent.
1. Since ABCD is a parallelogram, AD is congruent to BC, and DC is congruent to AB.
2. In addition, the two base angles for each of the opposite triangles are identical, for the parallelogram divides these angles equally on both sides.
3. Thus, by ASA, the opposite triangles are congruent.
4. Since CPCTC, this means that all sides of the opposite triangle are congruent.
5. This means that all opposite sides of PQST are congruent.
6. Since all opposite sides are congruent, PQST is a parallelogram.
