In the figure, DE||AC and DF||AE. Prove that \( \dfrac{BF}{FE}=\dfrac{BE}{EC}\)

In fig. DE||AC and DF||AE. prove that BF/FE = BE/EC

Asked by Pragya Singh | 1 year ago |  54

1 Answer

Solution :-

In ΔABC, given as, DE || AC

Thus, by using Basic Proportionality Theorem, we get,

\( \dfrac{BD}{DA}=\dfrac{BE}{EC}\)…………………(i)

In  ΔBAE, given as, DF || AE

Thus, by using Basic Proportionality Theorem, we get,

\( \dfrac{BD}{DA}=\dfrac{BF}{FE}\)  ………………(ii)

From equation (i) and (ii), we get

\( \dfrac{BE}{EC}\) = \( \dfrac{BF}{FE}\)

Hence, proved.

Answered by Abhisek | 1 year ago

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