Valerie is going to use SAS to prove that triangle VWX is congruent to triangle YZX, which of these is a necessary dye in Valerie’s proof

You are correct in selecting choice A as the answer. You need the middle angles between the two pairs of given congruent sides, so that you can prove the triangles to be congruent through SAS. The vertical angle theorem is used in this case. Alternate interior angles only come from parallel lines, but we dont know if any of the lines are parallel. Even if we did know the lines were paralle, we still wouldn't use the alternate interior angle theorem.