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Question 4In ...

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

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Solution

$I n Δ A B C, D E | | A C (G i v e n)$

$∴ \frac{B D}{D A} = \frac{B E}{E C} . . . (i) [B y u s i n g B a s i c P r o p o r t i o n a l i t y T h e o r e m]$

$I n Δ A B E, D F | | A E (G i v e n)$
$∴ \frac{B D}{D A} = \frac{B F}{F E} . . . (i i) [B y u s i n g B a s i c P r o p o r t i o n a l i t y T h e o r e m]$

From equation $(i)$ and $(i i)$ , we get,

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

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Similar questions

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

Q. 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}

.

Q. In the given figure

D E ∥ A C

D F ∥ A E

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

Q. Question 4
In figure,

B A ⊥ A C, D E ⊥ D F

such that BA =DE and BF =EC. Show that

Δ A B C ≅ Δ D E F

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