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.