1. The problem asks which triangle congruence theorem can be used to prove that two triangles are congruent in a parallelogram with diagonal DF. 2. In a parallelogram, opposite sides are equal and opposite angles are equal. The diagonal divides the parallelogram into two triangles. 3. The triangles formed by diagonal DF are \(\triangle DFG\) and \(\triangle DEF\). 4. Since \(DE = FG\) (opposite sides of parallelogram), \(DF\) is common to both triangles, and angles \(\angle EDF = \angle GFD\) are equal (alternate interior angles or opposite angles), we have two sides and the included angle equal. 5. This matches the SAS (Side-Angle-Side) congruence theorem, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. 6. Therefore, the SAS theorem can be used to prove the triangles are congruent.