Final answer:
The correct justification for the similarity between triangles △AEB and △DEC, given that ∠AED = ∠BEC, is AAA (Angle-Angle-Angle) similarity. This choice is correct as it relies solely on the equality of angles, which is the only information provided.
Step-by-step explanation:
The student's question asks for the justification of the similarity between two triangles, △AEB and △DEC, given that ∠AED = ∠BEC. Since we only have information about one pair of angles being equal, we can determine the similarity of the two triangles based on angle similarity.
The correct justification for the similarity of the two triangles is AAA (Angle-Angle-Angle) similarity, which states that if two triangles have two angles equal, the third angles are also equal by the Angle Sum Property of triangles making all corresponding angles equal, thus ensuring the triangles are similar.
However, based on the instructions given, no additional information is provided about the sides or angles, and therefore we cannot justify using SAS (Side-Angle-Side), SSS (Side-Side-Side), nor ASA (Angle-Side-Angle) similarity. Hence, the correct answer to the given question is option c) AAA (Angle-Angle-Angle) similarity.