Question

$PQR$ is a triangle in which $PQ=PR$ and $S$ is any point on the side $PQ.$ Through $S$, a line is drawn parallel to $QR$ and intersecting $PR$ at $T$. proves that $PS=PT$.

Answer 1

In $\Delta PQR$, we have

$PQ=PR\Rightarrow \angle R=\angle Q$

Now, $ST\parallel QR$.

$\Rightarrow \angle PST=\angle PQR$ and $\angle PTS=\angle PRQ$ [$\because$ Corresponding angles are equal]

$\Rightarrow \angle PST=\angle Q$ and $\angle PTS=\angle R$

$\Rightarrow \angle PST=\angle PTS$

$\Rightarrow PT=PS$