In AAS congruence, which parts are congruent?

• A. Two angles and the included side
• B. Two angles and the non-included side
• C. Two sides and the included angle
• D. All three sides

Answer: (B)

Two angles fix a triangle’s shape because the sum of angles in a triangle is always the same, so once two angles are known, the third is determined. If two angles in one triangle match two angles in another, the triangles are similar. The extra piece of information—the corresponding side that is not between the two equal angles—sets the size, turning similarity into congruence since the scale factor is fixed to 1. In other words, two angles plus a non-included side uniquely determines the triangle, so the triangles are congruent. (If the side given were the included side, that would be the ASA case, which is a different valid criterion.)