△ABC与△A1B1C1中,AD,A1D1分别是它们的中线,且AB/A1B1=AD/A1D1=AC/A1C1,求证：△ABC∽△A1B1C1

题目

△ABC与△A1B1C1中,AD,A1D1分别是它们的中线,且AB/A1B1=AD/A1D1=AC/A1C1,求证：△ABC∽△A1B1C1

答案

 如图,分别延长AD、A'D'至E、E',使DE=AD,D'E'=A'D',则AD/A'D'=AE/A'E',△ACD≌△EBD得BE=AC,∠E=∠EAC,同理B'E'=A'C',∠E'=∠E'A'C&...