Question

In the given figure, DE || AC and DF || AE. Prove that : `(BF)/(FE) = (BE)/(EC)`.

Answer 1

Given: D is any point on side AB of ΔABC and E and F are two points on side BC. The line segment DF, DE and AE are drawn.

To prove: `(BF)/(FE) = (BE)/(EC)`

Proof: In ΔABE, it is given that DF || AE.

Applying Basic Proportionality Theorem:

`(BD)/(DA) = (BF)/(FE)`   ...(i)

In ΔABC, it is given that DE || AC.

Applying Basic Proportionality Theorem:

`(BD)/(DA) = (BE)/(EC)`   ...(ii)

From equations (i) and (ii), we observe that the Left Hand Side (LHS) is identical for both:

`(BF)/(FE) = (BE)/(EC)`

Hence proved.