Yes
Reason : you can prove ABCD is a parallelogram from that two facts.
Proof:
Triangles ABE and CDE are congruent. (SAS)
Therefore, AB = CD and by writing the equal angles, you will get AB//CD.
Do the same for triangles ADE and BCE.
You'll get AD = BC and AD//BC
Hence, ABCD is a parallelogram.
