∴AB=BC=CD=AD,∠A=∠B=∠C=∠D
AE = BF = CM = DN。
∴BE=CF=DM=AN
∴△AEN≌△DNM≌△CMF≌△BFE
∴EN=NM=MF=EF
∴ quadrilateral EFMN is a diamond.
∠∠EFB+∠FEB = 90 degrees
And < nea+< feb = 90 degrees.
∴∠NEF=90 degree
∴ quadrilateral EFMN is a square.