Question

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

Answer 1

Given- In Triangle ABC ,DE ll AC and DF ll AE.

To Prove - BF/FE= BE/EC

Proof - In Triangle ABC,

Using BASIC PROPORTIONALITY THEOREM,

DE ll AC (given) (eqn. 1)

BD/DA = BE/EC

In Triangle ABE,

DFll AE

Using the BASIC PROPORTIONALITY THEOREM,we have

BD/DA= BF/FE (equation 2)

From Equations 1 and 2, we get

BF/FE=BD/DA= BE/EC

=  BF/FE = BE/EC