Final answer:
For triangle ABC to be congruent to triangle DEF by ASA, a statement establishing the equality of the included side between two pairs of equal angles from each triangle is required.
Step-by-step explanation:
To show that triangle ABC is congruent to triangle DEF by ASA (Angle-Side-Angle), we need to know that two angles and the included side of one triangle are respectively equal to two angles and the included side of the other triangle. For example, we could have angle A equal to angle D, angle B equal to angle E, and side AB (the side included between angles A and B) equal to side DE (the side included between angles D and E).
Any additional statement that provides this last piece of corresponding congruency (the side) in addition to the two pairs of equal angles would allow us to prove the congruence of the two triangles by ASA.