This is stumping me. it's a geometry proof question, and i really need ! diagram and statements are attached in a picture.

We know : 
To prove: AD = CD
AB = CB
angle BEA = angle BEC
BE = BE (common side)
So, by SAS criterion (Side-Angle-Side),
ΔBEA congruent to ΔBEC. 
By seeing the corresponding parts of the Congruent triangles, we observe:
AE = CE 
So, 
in triangles AED and CED,
ED = ED (common side)
AE = CE (given)
angle AED = angle CED 
So, by SAS criterion:
ΔAED is congruent to ΔCED.
Therefore, by observing the corresponding parts of congruent triangles,
we can say that: AD = CD.