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Basic Proportionality Theorem

Question 3In ...

Question

Question 3
In the following figure, if LM || CB and LN || CD, prove that $\frac{A M}{A B} = \frac{A N}{A D}$ .

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Solution

In the given figure, LM || CB
By using basic proportionality theorem, we get,
$\frac{M B}{A M} = \frac{L C}{A L}$
$\frac{M B}{A M} + 1 = \frac{L C}{A L} + 1$
$\frac{A B}{A M} = \frac{A C}{A L} . . . (i)$
Similarly, LN || CD
$∴ \frac{N D}{A N} = \frac{L C}{A L}$
$\frac{N D}{A N} + 1 = \frac{L C}{A L} + 1$
$\frac{A D}{A N} = \frac{A C}{A L}$ ... (ii)
From (i) and (ii), we get
$\frac{A B}{A M} = \frac{A D}{A N}$ or
$\frac{A M}{A B} = \frac{A N}{A D}$

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Basic Proportionality Theorem

Standard X Mathematics

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