Ok, so
We know that WZ and ZY are perpendicular, so XY and ZY has to be also perpendicular.
We also know that WY and XZ are similar sides, so:
Since 2 sides are congruent, they share a side and they are right triangles, by Pythagoras's theorem the third sides are also congruent. Both triangles share the ZY side, both have a 90° angle, and WY=XZ.
Question 2
ok, so
We know that all sides of a square are equal.
Notice that the diagonal, divides the square in two equal triangles.
As the triangles are equal, (because the hypotenuse is the same for both), both triangles are congruent.