Question

In the following figure, DE || AC and DF || AE. Prove that $\frac{BF}{FE}=\frac{BE}{EC}$.

Answer 1

To Prove: $\frac{BF}{FE}=\frac{BE}{EC}$

Proof:

In ∆ABC, DE || AC
∴$\frac{BD}{DA}=\frac{BE}{EC}$ (Basic proportionality theorem)......(i)

In ∆BAE, DF||AE
∴$\frac{BE}{EC}=\frac{BF}{FE}$ (Basic proportionality theorem)......(ii)

From (i) and (ii), we obtain,
$\frac{BF}{FE}=\frac{BE}{EC}$

Hence Proved.