如圖所示,在平行四邊形ABCD的對角線上AC上取兩點E和F,若AE=CF.求證:∠AFD=∠CEB.

如圖所示,在平行四邊形ABCD的對角線上AC上取兩點E和F,若AE=CF.求證:∠AFD=∠CEB.

證明:四邊形ABCD是平行四邊形,∵AD‖BC,AD=BC,∴∠DAF=∠BCE,∵AE=CF,∴AE+EF=CF+EF,即AF=CE,∴△ADF≌△CBE,∴∠AFD=∠CEB.