The quadrilateral ABCD is a rectangle,

The quadrilateral ABCD is a rectangle,

(1) It is proved that the ∵ quadrilateral ABCD is a rectangle,
∴AB∥CD,
∴∠ACD=∠CAB,
∵∠EDC=∠CAB,
∴∠EDC=∠ACD,
∴AC∥DE；
A quadrilateral BCEF is a parallelogram for the following reasons:
∵ BF ⊥ AC, the quadrilateral ABCD is a rectangle,
∴∠DEC=∠AFB=90°,DC=AB
In △ CDE and △ BAF,
∠DEC=∠AFB∠EDC=∠BAFCD=BA
,
∴△CDE≌△BAF（AAS）,
{CE = BF, de = AF (the corresponding sides of congruent triangles are equal),
∵AC∥DE,
That is, de = AF, de ‖ AF,
A quadrilateral ADEF is a parallelogram,
∴AD=EF,
∵AD=BC,
∴EF=BC,
∵CE=BF,
A quadrilateral BCEF is a parallelogram