如图,在△ABC中,DE∥BC,AD/BD=AE/EC,求证:AD/AB=AE/AC

问题描述:

如图,在△ABC中,DE∥BC,AD/BD=AE/EC,求证:AD/AB=AE/AC

证明:
∵AD/BD=AE/EC
∴BD/AD=EC/AE
=>BD/AD+1=EC/AE+1
=>BD/AD+AD/AD=EC/AE+AE/AE
=>(BD+AD)/AD=(EC+AE)/AE
=>AB/AD=AC/AE
∴AD/AB=AE/AC