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.