State whether true or false.

In the given figure $D E ∥ A C$ and $D F ∥ A E$ . Then $\frac{B F}{F E} = \frac{B E}{E C}$

True

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False

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Solution

The correct option is A True
In $Δ A B E$

$D F | | A E$

By Basic Proportionality theorem ,

$\frac{B F}{F E} = \frac{B D}{D A} \dots (1)$

In $Δ A B C$

$D E | | A C$

By Basic Proportionality theorem ,

$\frac{B E}{E C} = \frac{B D}{D A} \dots (2)$

From $(1), (2)$

$⟹ \frac{B F}{F E} = \frac{B E}{E C}$

Suggest Corrections

Similar questions

D E ∥ A C

D F ∥ A E

\frac{B F}{F E} = \frac{B E}{E C}

\frac{B F}{F E} = \frac{B E}{E C}

Question 4
In the following figure, DE||AC and DF||AE. Prove that $\frac{B F}{F E} = \frac{B E}{E C}$ .

Question 4
In the following figure, DE||AC and DF||AE. Prove that $\frac{B F}{F E} = \frac{B E}{E C}$ .

D E | | A C

D F | | A E

\frac{B F}{F E} = \frac{B E}{E C}

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