DE=23,AF=23×2=43,
∵ Quadrilateral ABCD is a square with a side length of 2.
∴∠DAB=90,AE=2-23=43,
∴AE=AF,
△ AEF is an isosceles right triangle.
(2) The quadrilateral ABCD is a square with a side length of 2,
∴AD=BC=2,
When the point f moves to the edge BC and AE=BF,
And then DE=CF,
The quadrilateral EFCD is rectangular,
∴EF∥CD,
∫AE = 2-t,BF=2t-2,
∴2-t=2t-2,
∴t=43,
When t = 43, the line segment EF is parallel to DC.
(3) According to (2), AE=2-t,
∫CF = 4-2t,
∴AECF=2? t4? 2t= 12,
∵ quadrilateral ABCD is a square,
∴AD∥BC,AB∥DC,
∴△AME∽△CMF,△AMN∽△CMD,
∴AMCM=AECF= 12,
∴ANCD=AMCM= 12,
∴AN= 12AB,
∴ANNB= 1.