Question

In the following figure, if LM || CB and LN || CD, prove that $\frac{AM}{AB}=\frac{AN}{AD}$.

Answer 1

In the given figure, LM || CB
By using basic proportionality theorem, we get,
$\frac{MB}{AM}=\frac{LC}{AL}$
$\frac{MB}{AM}+1=\frac{LC}{AL}+1$
$\frac{AB}{AM}=\frac{AC}{AL}...\left(i\right)$
Similarly, LN || CD
$\therefore \frac{ND}{AN}=\frac{LC}{AL}$
$\frac{ND}{AN}+1=\frac{LC}{AL}+1$
$\frac{AD}{AN}=\frac{AC}{AL}$ ... (ii)
From (i) and (ii), we get
$\frac{AB}{AM}=\frac{AD}{AN}$ or
$\frac{AM}{AB}=\frac{AN}{AD}$