∵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.