Quadrilateral AEFD is convex, with midpoints B and C of sides located, and segment drawn.(...

Quadrilateral AEFD is convex, with midpoints B and C of sides located, and segment drawn.

(a) If ABCD is a rectangle, show that BEFC and AEFD are rectangles.

(b) If AEFD is a rectangle, show that ABCD is a rectangle. (For this part you may "borrow" the result, proven later in Problem 18, that the opposite sides of a rectangle are congruent.)