Final answer:
To prove triangles congruent by AAS, we need two angles and a non-included side. Assuming one angle and one side are known, the measure of another non-adjacent angle (A, B, or C) is needed to apply AAS.
Step-by-step explanation:
To prove triangles congruent by the Angle-Angle-Side (AAS) Congruence Theorem, we must know two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle. If one angle and one side are already known, the additional information required would be the measure of another angle that is not adjacent to the known side. Since the AAS theorem requires two angles, knowing the measure of angle A, angle B, or angle C could serve as the necessary second angle, provided it is not next to the already known angle. Knowing the measure of angle D would not be immediately helpful if it is the angle adjacent to the side already mentioned. Without loss of generality, if we know the side is BC, angle C, then to use AAS, we would need the measure of either angle A or angle B, but not angle D, as it may be adjacent to the side BC.