如图,在三角形ABC的边AB,AC上分别取D,E两点,使BD=CE,DE延长线交BC的延长线于点F
问题描述:
如图,在三角形ABC的边AB,AC上分别取D,E两点,使BD=CE,DE延长线交BC的延长线于点F
求证DF/EF=AC/AB
答
做DF平行于AC,交BC于F,
根据相似三角形得:
EF/DF=EC/DF
DB/DF=AB/AC
又因为:DB=EC
所以:EF/DF=EC/DF=DB/DF=AB/AC
AC·EF=AB·DF
即:DF/EF=AC/AB