If a quadrilateral has consecutive angles that are supplementary, is the quadrilateral necessarily a parallelogram?

A quadrilateral has opposite sides that are parallel, but its diagonals do not bisect each other. Is this quadrilateral a parallelogram?

If the diagonals of a quadrilateral are of unequal length and do not bisect each other, can the quadrilateral still be a parallelogram?

If a quadrilateral has diagonals that are perpendicular bisectors of each other, is it necessarily a parallelogram?

In a quadrilateral, if one pair of opposite angles is both equal and supplementary, is the quadrilateral a parallelogram?

 If the diagonals of a quadrilateral bisect each other and are of equal length, can we conclude that the quadrilateral is a parallelogram?

 In a quadrilateral, if one pair of opposite sides is both parallel and equal in length, is the quadrilateral a parallelogram?

A quadrilateral has opposite angles that are supplementary. Is this quadrilateral a parallelogram?

A quadrilateral has consecutive sides with equal lengths, but its diagonals are not necessarily equal. Is this quadrilateral a parallelogram?

If a quadrilateral has opposite sides that are parallel and equal in length, can we conclude that it is a parallelogram?