To determine whether these quadrilaterals are parallelograms, we need to analyze their characteristics according to the definition of a parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent.
1. For the first quadrilateral (ABCD with diagonals intersecting at E), we are given that AB is congruent to AD and that AB is parallel to DC. If AB is parallel to DC, and AB is congruent to AD, then we have opposite sides that are parallel and congruent. Therefore, this quadrilateral is indeed a parallelogram.
2. In the second quadrilateral (ABCD with diagonals intersecting at E), it is given that AB and DC are congruent and parallel. This means that opposite sides are parallel and congruent, fulfilling the conditions of a parallelogram. Therefore, this quadrilateral is also a parallelogram.
3. For the third quadrilateral (ABCD with diagonals intersecting at E), it is only mentioned that DE and BE are congruent. However, we're not given any information about the parallelism of the sides. Without information about the parallel nature of the sides, we cannot conclude whether the quadrilateral is a parallelogram based solely on this condition.
In summary, based on the given conditions, the first two quadrilaterals are parallelograms, but we cannot determine whether the third quadrilateral is a parallelogram without additional information.