1)
Looking at the question, the given information about corresponding parts is that the corresponding sides are parallel.
2)
Since we don't have information about the length of any side, so the only theorem that may be used is AA case (angle-angle). Since we have parallel lines, we can try to find corresponding or alternate angles, since they are congruent angles.
3)
We need at least two pairs of congruent angles in the triangles.
4)
If we take two pairs of parallel sides, we can create a parallelogram. Since opposite sides in a parallelogram are congruent, so the angle created by adjacent sides in a triangle will be congruent to the angle created by the corresponding parallel sides in the other triangle.
This way, we can prove that each corresponding angles are congruent, therefore proving the similarity with AA case.