If two triangles have three congruent, corresponding angles, what additional information is needed to prove
that the triangles are congruent?

  a pair of corresponding sides must be shown congruent

Step-by-step explanation:

The triangles are "similar" if corresponding angles are congruent. The triangles will only be "congruent" if corresponding sides are also congruent. The additional information needed is that there is one congruent pair of corresponding sides. (If there's one pair, all pairs of corresponding sides will be congruent.)

Having one pair of corresponding sides congruent would allow you to invoke either of the ASA or AAS congruence postulates.

1/4 is the answer if i recall correctly.