Question 529246
I don't think so.
Suppose v=u, so that you really know vw and uw are congruent.
Make vw (or uw, since it is the same segment) the diameter of a circle.
Make x and y any of the other infinity of points on that circle.
Angle x and angle z measure 90 degrees and are congruent no matter how you chose x and y, but you can make many different non-congruent triangles.