Final answer:
Without angles or the third side measurement, we cannot apply congruency postulates (SSS, SAS, ASA) to prove that AB = DC, so the answer is D, not enough information.
Step-by-step explanation:
To determine whether AB = DC, we must apply a geometric theorem concerning congruent triangles. Given that AE = CE and DE = BE, by the reflexive property, AE = CE, which is a side in both triangles ABE and CDE. Similarly, DE and BE are also sides of these triangles. However, we are given no information about the angles within the triangles or the third side (AB and DC), so we cannot apply the Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA) congruency postulates or theorems to these triangles. Without additional information, particularly about the angles associated with DE and BE or the actual length of AB and DC, we cannot prove that AB = DC, indicating option D, not enough information, is correct.