如图,△ABC中,DE//BC,AD/BD=AE/EC,求证EC/AC=BD/AB
问题描述：
如图,△ABC中,DE//BC,AD/BD=AE/EC,求证EC/AC=BD/AB
答
证明：
设AD/BD=AE/EC=k,
则AD=kBD,AE=kEC,
则AB=AD+BD=(k+1)BD,AC=AE+EC=(k+1)EC,
∴EC/AC=1/(k+1),BD/AB=1/(k+1),
∴EC/AC=BD/AB
得证