Question

In given figure, If PS||QR, prove that $△POS\sim △ROQ$.

Answer 1

We have,

$PS||QR$

and transversal PR cuts them at P and R.

$\therefore$ $\angle 3=\angle 4$

Again, PS||QR and transversal SQ cuts them at S and Q

$\therefore$ $\angle 1=\angle 2$ also

$\angle 5=\angle 6$

Thus, in $△POS$ and $QOR$, we have

$\angle 1=\angle 2$ i.e., $\angle S=\angle Q$

$\angle 3=\angle 4$ i.e., $\angle P=\angle R$ and

$\angle 5=\angle 6$ i.e., $\angle POS=\angle QOR$

Therefore, by AAA-criterion of similarity, we have

$△POS\sim △ROQ$. $\left[Henceproved\right]$