Question

In fig.

$DE||AC$ and $DF||AE.$ prove that
$\frac{BF}{FE}=\frac{BE}{EC}$

Answer 1

In $\Delta ABC$

$DE||AC$

Line drawn parallel to one side of triangle, insects the other two sides. It divides the other side in same ratio.

$\frac{BE}{EC}=\frac{BD}{DA}$ __(i)

In $\Delta AEB$

$DF||AE$

Line drawn parallel to one side of triangle, intersects the other sides. It divides the other sides in same ratio.

$\frac{BF}{FE}=\frac{BD}{DA}$ __(ii)

From (i) & (ii)

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

$\therefore$ Hence proved.