Question

如图,AC、BD相交于O,AE=FC,AO=OC,BO=OD,求证∠1=∠2

Answer 1

因为AO=OC,BO=OD,且∠AOB与∠COD是对顶角,根据边角边原理知△AOB与△COD全等.因此AB//CD,即∠CDB=∠ABD.又AE=FC,AO=OC所以EO=FO,同上边角边原理可知△EOB与△FOD全等,即∠FDB=∠EBD.

∠1=∠ABD-∠EBD=∠CDB-∠FDB=∠2.结论得证