Question

矩形ABCD,EF垂直平分AC交AD于E,交BC于F,交AC于O (1)求证四边形AFCE是菱形 (2)若AB=4,BC

Answer 1

1、因△COF和△AOE中有：∠EAO＝∠FCO、∠AOE＝∠COF、OA＝OC

所以△COF和△AOE全等,所以OF＝OE

又△OAF和△OCE中有：OA＝OC、OE＝OF、∠AOF＝∠COE

所以△OAF和△OCE全等,所以∠FAO＝∠ECO,所以AF平行CE

又AE平行FC

所以四边形AFCE是菱形.