Answer:
To prove that FAB is congruent to ECD, we need to show that they have the same size and shape. Since ABCD is a parallelogram and FBED is a parallelogram, we know that opposite sides of these figures are parallel and equal in length. This means that AB is parallel to ED and is equal in length to ED. Similarly, FB is parallel to DC and is equal in length to DC. Therefore, FAB is congruent to ECD because they have the same size and shape.
Another way to prove this is to use the fact that a diagonal of a parallelogram divides the parallelogram into two congruent triangles. In this case, the diagonal AC of the parallelogram ABCD divides it into two congruent triangles, namely triangles ABC and ACD. Similarly, the diagonal BE of the parallelogram FBED divides it into two congruent triangles, namely triangles BEF and BED. Since triangles ABC and BEF are congruent, and triangles ACD and BED are congruent, we can conclude that FAB is congruent to ECD because they are both composed of two congruent triangles.