Question

已知：如图，在□ABCD中，线段EF分别交AD、AC、BC于点E、O、F，

EF⊥AC，AO＝CO．

（1）求证：△ABF≌△CDE；

（2）在本题的已知条件中，有一个条件如果去掉，并不影响（1）的证明，你认为这个多余的条件是            （直接写出这个条件）．

 

Answer 1

解：（1）∵四边形ABCD是平行四边形，

∴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