No, there is more than one right triangle with a hypotenuse equal to a given length.
I suggest you try to use your intuition on the simpler geometry questions. Ask yourself whether the given information is enough to determine a unique triangle. You have ASA (angle, side, angle) for two triangles, yes that forces the other two sides and the 3rd angle to be equal. So ASA ==> congruent. You have SSA? That first side, if it's long enough, can intersect the 3rd side in two different places, as so SSA doesn't give you congruence because the triangle, in general, won't be unique.