Question

What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem?

LO ≅ LM
OA ≅ MA
LOA ≅ LMA
LAO ≅ LAM

Answer 1

answer is 

LOA ≅ LMA

to prove that the triangles are congruent using the AAS congruence 

Answer 2

The correct answer is:

∠LOA ≅ ∠LMA

Explanation:

AAS, or angle-angle-side, states that if two angles and the non-included side of one triangle are congruent to the corresponding two angles and non-included side of a second triangle, then the triangles are congruent.

We have an angle and a side.  Out of the remaining two angles, the ones that would make the side marked, LA, non-included are LOA and LMA.  This must be the missing information.