Question

In $△ABC$ the points $M$ and $N$ are on $AB$ and $AC$. If $AB=1.3cm,AC=2.6cm,AM=0.5cm,AN=1.0cm$ then show that $MN\parallel BC$ or not?

Answer 1

In $△ABC$,
$\frac{AB}{AM}=\frac{1.3}{0.55}$
and $\frac{AC}{AN}=\frac{2.6}{1.0}\ne \frac{1.3}{0.55}$
Since, $\frac{AB}{AM}\ne \frac{AC}{AN}$

$\therefore$ By basic proprtionality theorem,
$MN$ is not parallel to $BC$.