Question

what additional information is needed to prove that the triangles are congruent using the aas congruence theorem? ∠lao≅∠lam, (overline{lo}congoverline{lm}), ∠loa≅∠lma, (overline{oa}congoverline{ma})

Explanation:

The AAS (Angle - Angle - Side) congruence theorem states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, the triangles are congruent. In the given triangles, we already have one pair of angles (the ones at vertex L) and a side (the common side LA). We need another pair of non - included angles. Among the options, $\angle LOA\cong\angle LMA$ provides the required additional pair of non - included angles.

Answer:

$\angle LOA\cong\angle LMA$