Question

DE || AC and DF || AE. Prove that
BF/FE=BE/EC
​

Answer 1

Given:

In Triangle ABC

DE // AC.

To Prove That:

BF/FE=BE/EC

Proof:

By Basic Proportionality Theorem:

BD/DA = BE/EC………. Equation (i)

Again by Basic Proportionality Theorem:

BD/DA = BF/FE……….Equation (ii)

From Equation (i) and Equation (ii):

BE/EC = BF/FE

Hence proved.

Answer 2

Answer:

In triangle ABC, DE parallel to AC,

.°. BD / DA = BE / EC ...(1) (by basic property theorem)

In triangle ABE, DF parallel to AE,

.°. BD / DA = BF / FE ...(2) (by basic property theorem)

From (1) and (2), we get

BF / FE = BE / EC, as required.