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

In \( \triangle ABC\), given as, DE || AC

Thus, by using Basic Proportionality Theorem, we get,

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

In \( \triangle ABC\), given as, DF || AE

Thus, by using Basic Proportionality Theorem, we get,

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

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

Hence, proved.