The parallelogram theorems are where a geometry student first strings the earlier pieces together: alternate interior angles, the reflexive property, a congruence criterion, then CPCTC. These free printable worksheets give the figure, the Given and the Prove, and leave the table blank.
If they get stuck
The answer key prints on a separate page.
Every proof of a parallelogram property runs the same road, and seeing that once is worth more than any single proof: draw a diagonal to make two triangles, use the parallel sides to find equal angles, notice the diagonal is shared, close with ASA or SSS, then read off the part you were asked for. The sheets cover the properties the standard names — opposite sides congruent, opposite angles congruent, and the diagonals bisecting each other.
The second setting is the CONVERSE, and it is the harder half. There the quadrilateral is not yet known to be a parallelogram; the proof establishes the triangles are congruent, uses CPCTC to get equal angles, and then turns those back into parallel sides with the converse of the alternate interior angle theorem — a step students routinely try to use in the wrong direction.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Parallelogram proofs, step by step