$PQR$ 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 $T$. Prove that $PS = PT$.

Given:

$PQR$ 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 $T$.

To do:

We have to prove that $PS = PT$.

Solution:

$PQ = PR$

This implies,

$\angle Q = \angle R$

$ST \parallel QR$

This implies,

$\angle S = \angle Q$                  (Corresponding angles)

$\angle T = \angle R$                  (Corresponding angles)

This implies,

$\angle S = \angle T$

Therefore,

$PS = PT$             (Sides opposite to equal angles are equal)

Hence proved.

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Updated on: 10-Oct-2022

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