全等三角形突破进阶难题5题
全等突破5题Bb C EA D F A1.【手拉手,中难】如图,等边ABC与等边DCE拥有公共顶点C.分别连接AE、BD、CF.(1)求证BD=AE;(2)求证CF平分BFE.Bb Ab Db Cb Eb 2.【倍长中线构全等,较难】如图,AD是ABC的中线,点E在BC的延长线上,CE=AB,BAC=BCA,求证:AE=2AD.Bb Cb Db Ab Eb Fb 3.【婆罗摩笈多模型/定理,较难】如图,AD是ABC的中线,AEAC,AFAB,且AE=AC,AF=AB.试判断AD与EF的关系,并给出证明.Bb Ab Db Eb Fb Cb 4.【全等垂直+中线+等腰综合模型,较难】如图,AB=AC,BACA于A,D为AC中点,AFBD于E,连接DF,求证ADB=CDF.Bb Eb Ab Db Cb Fb 5.【外半角模型,很难】如图,ACD为等边三角形,ABC为顶角ABC=120°的等腰三角形,EBF=60°,求证EF=CF-AE.