Question

In $\Delta$PQR, MN is parallel to QR and $\frac{PM}{MQ}=\frac{2}{3}$. Prove that $\Delta$OMN and $\Delta$ORQ are similar.

Answer 1

Given, $MN||QR$

In $△OMN\&△ORQ$

$\angle OMN=\angle ORQ$ (Alternate interior angles are equal)

$\angle ONM=\angle OQR$ (Alternate interior angles are equal)

$\angle MON=\angle QOR$(Vertically opposite angles are equal)

Thus, we have that $△OMN\sim △ORQ$ by $AAA$ test of similarity.

Hence Proved that the triangles $OMN$ and $OQQ$ are similar.