1. The problem is to determine if the two triangles shown are congruent and if yes, state the theorem that proves their congruence. 2. The common theorems to prove triangle congruence are: - SAS (Side-Angle-Side): Two sides and the included angle are congruent. - ASA (Angle-Side-Angle): Two angles and the included side are congruent. - AAS (Angle-Angle-Side): Two angles and a non-included side are congruent. - SSS (Side-Side-Side): All three sides are congruent. 3. From the description, the two triangles share a common side, and the left sides have two pairs of congruent segments marked. 4. This means two sides and the included angle between them are congruent. 5. Therefore, the triangles are congruent by the SAS theorem. Final answer: yes, SAS