What information could be helpful to determine if these triangles have corresponding congruent angles?
Are the triangles similar? No. Additional information: BC parallel to DF.
Practice makes perfect
Let's notice that △ ABC and △ ADF have one corresponding congruent angle as ∠ A≅ ∠ A by the Reflexive Property. Since we have no information about the side lengths, let's think how we can prove similarity using angle measures.
Now recall the Corresponding Angles Postulate.
If parallel lines are cut by a transversal,
then the pairs of corresponding angles
are congruent.
If we knew that BC is parallel to DF, then ∠ ABC and ∠ ADF would be congruent angles, just as ∠ ACB and ∠ AFD. That would prove the similarity by the Angle-Angle Similarity Postulate. However, since we do not have such information, we cannot determine if these triangles are similar.
