check the picture below.
since WZ is a bisector of the quadrilateral, that means, it makes two equal halves at the vertex Z and W, that means each triangle gets of those twin angles, so those two angles are the same for both triangles.
now, notice, the segment WZ is shared by both triangles, and thus the tickmark, is the same length for both.
so, you have on Angle and then a Side and then another Angle, two angles and the side between them equal in each triangle, thus congruents by ASA.
