Because AG//BC, angle EAG= angle ECF, angle AGE= angle EFC, angle AEG= angle CEF, AE=EC, it is concluded that triangle AGE and triangle CEF are two completely equal triangles, and then it is concluded that GE=EF and AG=FC.

In quadrilateral AGFB, FG//AB, AG//BC, AD=DB, GE=EF, so GE//AG//BC//FC, and DE=AG=BF=FC.