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20 14 two-mode mathematics in Huaiyin district
When (1)t=23,

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.