1. **State the problem:** Determine if the triangles are congruent and by which method (SSS, SAS, AAS, ASA) or if none applies. 2. **Given:** - Problem 1: Triangles \(\triangle ABF\) and \(\triangle CBI\) are congruent by ASA Postulate. - Problem 2: No congruency. - Problem 3: Congruent triangles by AAS Postulate. - Problem 4: No congruency. 3. **Explanation of methods:** - **SSS (Side-Side-Side):** Triangles are congruent if all three sides are equal. - **SAS (Side-Angle-Side):** Triangles are congruent if two sides and the included angle are equal. - **ASA (Angle-Side-Angle):** Triangles are congruent if two angles and the included side are equal. - **AAS (Angle-Angle-Side):** Triangles are congruent if two angles and a non-included side are equal. 4. **Apply to Problem 1:** - Method: ASA Postulate. - Congruent triangles: \(\triangle ABF \cong \triangle CBI\). 5. **Apply to Problem 2:** - No congruency deduced. 6. **Apply to Problem 3:** - Method: AAS Postulate. - Congruent triangles: (Not named in the problem, but congruent triangles exist by AAS). 7. **Apply to Problem 4:** - No congruency deduced. **Final answers:** - 1) Method: ASA, Triangles: \(\triangle ABF \cong \triangle CBI\) - 2) None - 3) Method: AAS, Triangles: congruent triangles by AAS - 4) None