Answer:
i am unsure how your options are like since there is no free response but heres my proof:
since ba and cd are parallel to ad, they must be parallel to each other.
now all we need to prove is that ad is parallel to bc
since bac and cdf are congruent, ab = dc meaning bc is parallel to ad
therefore with a right angle and 2 pairs of parallel sides, abcd is a rectangle
hope it helps