1. **Problem:** Which theorem or postulate can be used to show $\triangle GBE \cong \triangle ABD$? 2. **Recall the common triangle congruence postulates:** - SSS (Side-Side-Side): All three sides of one triangle are congruent to all three sides of another. - SAS (Side-Angle-Side): Two sides and the included angle of one triangle are congruent to two sides and the included angle of another. - ASA (Angle-Side-Angle): Two angles and the included side of one triangle are congruent to two angles and the included side of another. - AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are congruent to the corresponding parts of another. 3. **Analyze the triangles $\triangle GBE$ and $\triangle ABD$:** - Given the figure, the two triangles share side $BE = BD$ (assuming $E$ and $D$ are points on the same segment or equal segments). - Angles at $B$ are congruent (common angle). - Sides $GB$ and $AB$ are congruent (given or marked). 4. **Apply SAS postulate:** - Two sides and the included angle are congruent between the triangles. 5. **Conclusion:** The correct postulate is SAS. **Final answer:** $\boxed{\text{SAS}}$