Question

In the given figure, If $ML\parallel BC$ and $NL\parallel DC$, then $\frac{AM}{AB}=\frac{AN}{AD}$.

• A. True
• B. False

Answer 1

The correct option is A True

In $△ACB$

$LM\parallel CB$

$\frac{AL}{LC}=\frac{AM}{MB}$........(1)

In $△ACD$

$LN\parallel CD$

$\frac{AL}{LC}=\frac{AN}{ND}$........(2)

From (1) and (2), we have,

$\frac{AM}{MB}=\frac{AN}{ND}$

$\Rightarrow \frac{MB}{AM}=\frac{ND}{AN}$

$\frac{MB}{AM}+1=\frac{ND}{AN}+1$

$\frac{MB+AM}{AM}=\frac{ND+AN}{AN}$

$\frac{AB}{AM}=\frac{AD}{AN}$

$\therefore \frac{AM}{AB}=\frac{AN}{AD}$