Ratio between areas of parallelograms. 【Fun Math, 9th grade – 1】

This question comes from Germany mathematical Olympiad competition of 9th grade. Given a parallelogram ABCD, The midpoint of each side is labeled as E, F, G, and H, respectively. The connecting lines AG, BH, CE, and DF cut out a quadrilateral WXYZ inside the parallelogram. The task includes two parts. First, it is asked to prove that WXYZ is also a parallelogram. Second, it is asked to calculate the ratio of the area of this parallelogram WXYZ to that of the parallelogram ABCD.