No, the quadrilateral is not always a parallelogram
Step-by-step explanation:
Since there are only four opposite angles in a quadrilateral there are only two possible angle bisectors of the opposite angles also, the angle bisectors of a pair of opposite angles of a quadrilateral will intersect within the quadrilateral and therefore they cannot form the sides of a parallelogram
Therefore, the answer is no, the quadrilateral is not always a parallelogram.
