1. **Problem Statement:** Determine if triangles are congruent by ASA or AAS and match the correct congruence statement. 2. **Recall the criteria:** - 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. 3. **Analyze Graph 1 (Triangle J, K, L, M with diagonal KM):** - Angles at J and L are marked. - Diagonal KM is a side common to both triangles JKM and LKM. - Two angles and the included side KM are congruent. - Therefore, by ASA, \(\triangle JMK \cong \triangle LKM\). 4. **Analyze Graph 2 (Triangles ABD and CDE sharing point C):** - Angle marked at D. - Segments AB and AE marked equal. - Angles at B and E are not both given. - Insufficient information for ASA or AAS. - Conclusion: Not Possible. 5. **Analyze Graph 3 (Triangle FGH with altitude GH):** - Angles at G and at intersection of GH and FH marked. - Altitude GH is perpendicular, so right angle present. - Two angles and a side (GH) are congruent. - By AAS, \(\triangle FIG \cong \triangle HIG\). 6. **Analyze Graph 4 (Triangles ABD and CDE sharing point C):** - Segments AB and CE marked equal. - Angles at B and E marked. - Two angles and a non-included side are congruent. - By ASA, \(\triangle BCA \cong \triangle ECD\). **Final matches:** - Graph 1: \(\triangle JMK \cong \triangle LKM\) by ASA - Graph 2: Not Possible - Graph 3: \(\triangle FIG \cong \triangle HIG\) by AAS - Graph 4: \(\triangle BCA \cong \triangle ECD\) by ASA