解答:证明:(1)∵AD∥BC,DE=3,BC=6,∴
=DF FB
=DE BC
=3 6
,1 2
∴
=DF BD
,∵BD=6,∴DF=2.1 3
∵DA=4,∴
=DF DA
=2 4
,1 2
=DE DB
=3 6
.∴1 2
=DF DA
.DE DB
又∵∠EDF=∠BDA,∴△DFE∽△DAB.
(2)∵△DFE∽△DAB,∴
=EF AB
.DE DB
∵AB=5,∴
=EF 5
,∴EF=3 6
=2.5.5 2
∵DE∥BC,∴
=CF EF
.BC DE
∴
=CF 2.5
,∴CF=5.6 3
(或利用△CFB≌△BAD).