Question

初中平面几何证明题如图,AB‖CQ,AC‖BP,D为BC中点,G为AD中点,过G的直线交BP、CQ于E、F,交AB、AC

Answer 1

为了方遍用小写字母表示,过点G做BC的平行线交BP、CQ于s4,s1,交AB、AC于s3,s2.显然s1s3BC为平行四边形,s1s3=BC,Gs3=[1/4]BC,s1G/Gs3=3,FG=3GM,FN+NG=3GM,同理得到EG=3GN,EM+MG=3GN,FN+NG+EM+MG=3[GM+GN],FN+EM=2MN.证毕.