In the below figure DE||AC and DF||AE. Prove that \frac{BF}{FE} = \frac{BE}{EC}

Step 1: Examine the given figure and note down the given data
NOTE: In the given figure, DE || AC and DF || AE
Prove \frac{BF}{FE}=\frac{BD}{EG}
Step 2: Take the triangle based up on the given data
NOTE: DE || AC and DF || AE
So, take triangle ABC
(because we can apply basic proportionality theorem.)
Step 3: Apply the basic proportionality theorem to the triangle
EXAMPLE: In triangle ABC, when DE || AC.
\frac{BD}{DA} = \frac{BE}{EC} ......................(1)
In triangle ABC, when DF || AE
\frac{BD}{DA} = \frac{BF}{FE} . ........................(2)
Step 4: Prove the given ratio by using the equations
EXAMPLE: From the equations (1) and (2)
we get \frac{BF}{FE} = \frac{BE}{EC}