Question

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

LO ≅ LM
OA ≅ MA
AngleLOA ≅ AngleLMA
AngleLAO ≅ AngleLAM

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

Answer 1

AAS requires two angles and a non‑included side. You already have the side LA and the angle at L (∠OLA ≅ ∠ALM), so you need one more angle congruence. For example, add either

- ∠LOA ≅ ∠LMA

or

- ∠LAO ≅ ∠LAM.

With one of those added, you have two angles and the non‑included side, so ΔLOA ≅ ΔLAM by AAS.