Question

In $△$ ABC, D and E are points on sides AB and AC respectively such that AD $\times$ EC = AE $\times$ DB. Prove that DE $\parallel$ BC.

Answer 1

Given, $AD\times EC=$$AE\times DB$

$\therefore \frac{AD}{DB}=\frac{AE}{EC}$

By Coverse of basic Proportionality theorem, which states that

''If a line divides two lines of a $△$ in same ratio, then line is parallel to Third side.''

$DE\parallel BC$

Hence, proved.