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 $$PS = PT$$.

Solution

## 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 $$\angle PTS=\angle R$$$$\Rightarrow \angle PST=\angle PTS$$$$\Rightarrow PT=PS$$Mathematics

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