1. The problem asks which congruence rule explains why the two triangles inside the parallelogram are congruent. 2. The triangles share a common side and have pairs of congruent angles and sides marked. 3. The congruence rules to consider are AAS (Angle-Angle-Side) and SSS (Side-Side-Side). 4. AAS states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. 5. SSS states that if all three sides of one triangle are congruent to the corresponding sides of another triangle, the triangles are congruent. 6. In the given figure, the triangles share a side (common side), and two pairs of angles are congruent. 7. Since two angles and the non-included side are congruent, the AAS rule applies here. 8. Therefore, the triangles are congruent by the AAS rule.