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

Two corresponding angles and their including side are congruent.

Step-by-step explanation:

To prove that two triangles are congruent to each other by using ASA i. e. angle-side-angle congruence theorem, we need to prove that any two corresponding angles of the two triangles are equal and the side included by those two angles of the two triangles are equal.

For example if Δ ABC and Δ PQR are congruent by ASA criteria, then if ∠ A = ∠ P, ∠ B = ∠ Q and their including side AB and PQ are equal. (Answer)