Final answer:
To prove triangle congruence by ASA, you need to know two congruent angles and the length of the side between them in both triangles.
Step-by-step explanation:
To prove two triangles congruent by the Angle-Side-Angle (ASA) postulate, you must show that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle. The additional information you would need includes the measurements of two congruent angles in each triangle and the length of the side between them.
This included side must be the side that connects the two angles you have the measurements for.
Let's look at an example. If you know that ∆ABC and ∆DEF are two triangles where ∠A = ∠D and ∠B = ∠E, then the additional information needed to prove that these triangles are congruent by ASA is the length of side AB in ∆ABC and the length of side DE in ∆DEF. If AB is congruent to DE, then the triangles are congruent by ASA.