Final answer:
To prove ΔLMO ≅ ΔNMO by AAS, the congruence needed is LM ≅ MN (Option B), since we require two angles and the non-included side to be congruent.
Step-by-step explanation:
To prove that ΔLMO ≅ ΔNMO using the Angle-Angle-Side (AAS) Congruence Theorem, we need to show that two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in the other triangle.
If it is already given that two pairs of angles are congruent between the triangles (ΔLMO and ΔNMO), then we need to show that the corresponding non-included sides are congruent. The non-included side would be the one that does not connect the two angles already proven to be congruent.
Therefore, the correct answer is B) LM ≅ MN. Option A is incorrect since ∠LMO and ∠NMO are likely to be the same angle if LMO and NMO are names of the triangles sharing the vertex O. Option C is incorrect because LO and ON are sides of the triangles but not necessarily non-included sides relative to known congruent angles, and option D is incorrect because additional information is indeed needed to establish congruence.