Prove:

fold

So quadrilateral ABFE≌ quadrilateral A'DFE

∴∠EFB=∠EFD

700 BC

∴∠BFE=∠DEF

∴∠DEF=∠DFE

∴DE=DF

△ def is an isosceles triangle.

(2)

The quadrangle BEDF is a diamond, and BD and EF are equally divided vertically.

Prove:

fold

∴EF vertical division BD

∴FE=FD,EB=ED

And (1) can get DE=DF.

∴BE=ED=DF=FB

A quadrilateral is a diamond.