Which criterion uses two angles and the non-included side?

• A. ASA
• B. SSS
• C. SAS
• D. AAS

Answer: (D)

Two angles fix the shape of a triangle, since the third angle is automatically determined by the two. If you also know a side that is not between those two angles (a non-included side), that extra piece of information pins down the size and position of the triangle so that the two triangles must be identical in shape and size. This combination is the angle–angle–side criterion, which guarantees congruence.

So, knowing two angles plus a non-included side uniquely determines the triangle, making the two triangles congruent. The other criteria involve different arrangements: two angles with the included side (angle–side–angle) is a different rule, three sides (SSS) is another, and two sides with the included angle (SAS) is another.