Question

已知：如圖，在□ABCD中，線(xiàn)段EF分別交AD、AC、BC于點(diǎn)E、O、F，

EF⊥AC，AO＝CO．

（1）求證：△ABF≌△CDE；

（2）在本題的已知條件中，有一個(gè)條件如果去掉，并不影響（1）的證明，你認(rèn)為這個(gè)多余的條件是            （直接寫(xiě)出這個(gè)條件）．

 

Answer 1

解：（1）∵四邊形ABCD是平行四邊形，

∴AB＝CD，∠B＝∠D，AD＝BC，AD∥BC．

∵AD∥BC．

∴∠EAO＝∠FCO，

又∵∠AOE＝∠COF，

∴△AOE≌△COF．················································································· 3分

∴CF＝AE，

∴AD－AE＝BC－CF，

即DE＝BF．

∵AB＝CD，∠B＝∠D，BF＝DE，

∴△ABF≌△CDE．················································································· 5分

（2）EF⊥AC．······························································································ 7分