Point e is the midpoint of side bc of parallelogram abcd, and point f is the midpoint of side ad prove that quadrilateral afce is a parallelogram.

See proof below

Step-by-step explanation:

Theorem: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.

Consider parallelogram ABCD. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Thus, BC||AD. A parallelogram has 2 sets of opposite sides congruent. Thus, BC=AD.

If E and F are midpoints of sides BC and AD, then halves of these sides are congruent too (CE=FA).

In the quadrilateral AFCE, we have congruent and parallel sides EC and FA. Thus, this quadrilateral is a parallelogram.