Let's go through the answer choices one at a time.
A) The AA postulate is only used for similar triangles, and not congruent triangles. We need information about at least one pair of sides. Using the angles only isn't enough. We can rule out choice A.
B) The HL postulate only applies to right triangles. These triangles are acute triangles, so we can rule out choice B.
C) This is the answer as we can rule out choice D, so this is the only thing left. Also, if we know that angle A = angle A'' and angle B = angle B'', then we could use the ASA theorem to prove the triangles congruent.
D) This is not a valid congruence theorem. This is because we could have ambiguous cases that arise and lead to confusion. Also, it is possible that if we know two sides and a non-included angle, then a triangle may not be able to be formed. It will depend on the angle and side values. Therefore, we can rule out choice D.
