1. The problem is to understand the key difference between the ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) triangle congruence criteria. 2. Both ASA and AAS are used to prove that two triangles are congruent, meaning they have exactly the same size and shape. 3. ASA states that if two angles and the included side (the side between the two angles) of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. 4. AAS states that if two angles and a non-included side (a side that is not between the two angles) of one triangle are equal to the corresponding two angles and side of another triangle, then the triangles are congruent. 5. The key difference is the position of the known side: ASA requires the side to be between the two known angles, while AAS requires the side to be outside (not between) the two known angles. 6. Both criteria guarantee congruence because knowing two angles determines the third angle (since the sum of angles in a triangle is always $180^\circ$), and the side length helps fix the size. Final answer: The key difference is that ASA involves the side between the two angles, while AAS involves a side not between the two angles.