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

Explanation:

To prove congruence by AAS (Angle-Angle-Side), two angles and a non-included side must be congruent. Assuming triangles △LOA and △LMA share side LA (common, hence congruent), and if ∠LAO ≅ ∠LAM (angle at A), this provides one angle. With a common angle at L (∠OLA ≅ ∠MLA), two angles are established. The non-included side LA (common) completes AAS.

Answer:

∠LAO ≅ ∠LAM