Let's begin with recalling the Side-Angle-Side Congruence Postulate.
If two sides and the included angle
of one triangle are congruent
to two sides and the included angle
of a second triangle, then the triangles
are congruent.
Now, let's look at the given picture.
We are given that one angle is congruent but we know nothing about the sides that include this angle. Therefore, it is not possible to prove congruence in this case.