∵ABCD is a parallelogram.

∴AB//CD,AD//BC

AB=CD，AD=BC

∴∠DAB=∠DCB，

Vertical AB, vertical CD

∴∠DEA=90 =∠BFC

DE//BF

△AED，△BCF

∠DEA+∠EAD+∠ADE= 180

∠BCF+∠BFC+∠FBC= 180

∴∠ADE=∠CBF

∠∠DAB =∠DCB

AD = BC

∠ Adebayor =∠CBF

∴△AED and△ △BCF are congruent

∴AE=CF？ ( 1)

∵AB//CD, e is the point on AB, and f is the point on CD.

∴EB//DF

∫ in quadrilateral DEBF

EB//DF，DE//BF

∴ Quadrilateral DEBF is a parallelogram (2)?

note:

(2) It can also be proved that the DEBF of a quadrilateral is a square,

Vertical AB, vertical CD

∠ Debt =∠BFD=90

A quadrilateral is a square.

Or AM=CN,

Because this problem "diagonal AC and DE intersect at point M and BF intersect at point N" seems useless.