已知菱形ABCD的对角线AC,BD相交于点O,EF//AC,GH//AC,HE//BD,GH//BD交点分别为E,F,G,H求证;四边形EFGH为矩形

Question

已知菱形ABCD的对角线AC,BD相交于点O,EF//AC,GH//AC,HE//BD,GH//BD交点分别为E,F,G,H
求证;四边形EFGH为矩形

Answer 1

因为ABCD为菱形,所以AC垂直于BD,所以EF垂直于EH且EF//GH,EH//FG,所以EFGH为矩形