If your teacher is asking "which of the following can be used to prove the triangles congruent?" then I agree with your statement that it's "none of the above". We simply don't have enough information to determine if the triangles are congruent or not. If we wanted to use SAS, then we'd have to know if EB = BD was true. If we wanted ASA, then we'd have to know that A = C. If we wanted AAS, then we'd have to know that E = D.
In short, you have the correct answer. Nice work.
