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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.