So BO = OD∠OBH =∠GDF∠DOH =∠ God (this is a diagonal).

So △ Boh△ God AAS

Because BE=FD, EO=OF, and because OH=OG, there is a parallelogram EGFH (the quadrilaterals whose diagonals bisect each other are parallelograms).

So EG=HF, GF‖EH