证明：过A作BF的平行线AM,延长FD交AM于点G
AG//BF,
所以,角G=角F
D为AB的中点,所以AD=BD,
角ADG=角BDF,所以AGD全等于BFD,
所以,AG=BF
AG//BF,AEG相似于CEF,
所以,AE/EC=AG/CF
AE*CF=AG*EC,AG=BF
AE*CF=BF*EC