Question

Is the following enough information to show that quadrilateral ABCD is a parallelogram?

Imported Asset
Segment AE is congruent to Segment EC.
Segment BE is congruent to Segment ED.

Answer 1

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.