If a line intersects sides AB and AC of a $Δ A B C$ at D and E respectively and is parallel to BC, prove that $\frac{A D}{A B} = \frac{A E}{A C}$ . [2 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark

$D E ∥ B C$ (Given)

So, $\frac{A D}{D B} = \frac{A E}{E C}$ [Basic proportanality theorem]

$\frac{D B}{A D} = \frac{E C}{A E}$ [Taking reciprocal]

$\frac{D B}{A D} + 1 = \frac{E C}{A E} + 1$ [Adding 1 on both sides]

$\Rightarrow \frac{A B}{A D} = \frac{A C}{A E}$

$\Rightarrow \frac{A D}{A B} = \frac{A E}{A C}$

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