Question

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

Answer 1

$In\Delta ABC,DE||AC\left(Given\right)$

$\therefore \frac{BD}{DA}=\frac{BE}{EC}...\left(i\right)\left[ByusingBasicProportionalityTheorem\right]$

$In\Delta ABE,DF||AE\left(Given\right)$
$\therefore \frac{BD}{DA}=\frac{BF}{FE}...\left(ii\right)\left[ByusingBasicProportionalityTheorem\right]$

From equation $\left(i\right)$ and $\left(ii\right)$, we get,

$\frac{BE}{EC}=\frac{BF}{FE}$