Question

Given:In quadrilateral WXYZ , WY and XZ bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram.

Answer 1

These bisectors intersect each-other at 90 degrees. And it means that they are perpendicular. Since they are perpendicular, we find that there 4 congruent triangles and XY is parallel to WZ and WX is parallel to YZ. Additionally, opposite angles are equal. These two latter findings are the characteristics of the parallelogram.   

Answer 2

The figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent.