Final answer:
The triangles are congruent by the AAS (Angle-Angle-Side) postulate.
Step-by-step explanation:
The congruence postulate or theorem that shows the given triangles are congruent is AAS (Angle-Angle-Side).
To prove that two triangles are congruent using the AAS congruence postulate, we need to show that two angles and the included side of one triangle are congruent to the corresponding angles and side of the other triangle.
In the given triangles, if we can show that ∠B = ∠B₁ and ∠A = ∠A₁, and ∠O = ∠O, and AB = A₁B₁, then we can conclude that the triangles are congruent by the AAS postulate.