It is proved that connecting BE, crossing E is parallel to BF, crossing F is parallel to BE, two straight lines cross G point, connect AG, and then extend BE to cross AG at H point. rule
BF=EG,∠AEG=∠ECF
At △AEG and △ECF, AE/EC=EG/CF, ∠AEG=∠ECF,
So: two triangles are similar.
So: ∠EAG=∠CEF
So: AG‖DF
So: quadrilateral EFGH and quadrilateral BFGE are parallelograms.