Question

In the figure given below, $\angle PQR=\angle PRS$. Prove that triangles $PQR$ and $PRS$ are similar. If $PR=8cm,PS=4cm$, calculate $PQ$.

Answer 1

From the figure,

$\angle P=\angle P$ (common angle for both triangles)

$\angle PQR=\angle PRS$ [from the question]

So, $△PQR\sim △PRS$

Then, $PQ/PR=PR/PS=QR/SR$

Consider $PQ/PR=PR/PS$

$PQ/8=8/4$

$PQ=(8\times 8)/4$

$PQ=64/4$

$PQ=16cm$.