Question

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

Answer 1

Answer:

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Answer 2

S O L U T I O N :

Case (I),

In ∆ABC, DE || AC

According to the basic proportionality Theorem,

$\leadsto \pink{ \boxed{ \bold{ \dfrac{BD}{DA} = \dfrac{BE}{EC}}}} - - - - - (1)$

Case (II),

In ∆ABC, DE || AE

According to the basic proportionality Theorem,

$\leadsto\green{ \boxed{ \bold{ \dfrac{ BD}{DA }= \dfrac{BF}{FE}}}} - - - - - (2)$

From equation (1) and (2),

$\leadsto \red{ \boxed{\bold{ \dfrac{BE}{EC }= \dfrac{BF}{FE}}}}$

• Hence Proved!!