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The Mid-Point Theorem

If in a ABC...

Question

If in a $△ A B C, D E ∥ B C$ and intersects $A B$ in $D$ and $A C$ in $E$ , then match the following.

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Solution

Given : $D E ∥ B C$
$∠ A = ∠ A$ (Common.)
$∴$ $△ A D E ≅ △ A B C .$
$i)$ $\frac{A D}{D B} = \frac{A E}{E C}$
$i i)$ $\frac{A B}{A D} = \frac{A C}{A E}$
$i i)$ $\frac{D B}{A B} = \frac{E C}{A C}$
$i v)$ $\frac{A D}{A B} = \frac{A E}{A C}$

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