It is known that quadrilateral ABCD is a parallelogram with AC=BD.

Verification: ∠ ADC = 90

It is proved that∵ quadrilateral ABCD is a parallelogram.

? ∴AD=BC,AD∥BC

? ∴∠ADC+∠BCD= 180

? AC = BD，DC=CD

? ∴△ADC≌△BCD(SSS)

? ∴∠ADC=∠BCD

? ∴∠ADC=90

4.( 1) Yes

The reason is that point E and point F move from point A and point C to point O at the same speed respectively.

? ∴AE=CF

? ∵ Quadrilateral ABCD is a parallelogram

? ∴OA=OC,OB=OD

? ∴OE=OF

? A quadrilateral is a parallelogram.

(2) When the quadrilateral DEBF is rectangular,

∴OE=OB=OF=OD

? ∴EF= 10cm

? ∫BD = 10cm，AC= 16cm

? ∴AE+CF=6cm

AE = CF

? ∴AE=CF=3cm

? ∫ The moving speed of point E and point F is1cm/s.

? When t=3s, the DEBF of a quadrilateral is a rectangle.