Given a parallelogram abcd. diagonals ac and bd intersect at e. we have to prove that ae is congruent to ce and be is congruent to de. diagonals of parallelogram bisect each other.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.