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In the figure, $PQRS$ is a square and $SRT$ is an equilateral triangle. Prove that $PT = QT$.
"
Given:
$PQRS$ is a square and $SRT$ is an equilateral triangle.
To do:
We have to prove that $PT = QT$.
Solution:
In $\triangle TSP$ and $\triangle TQR$,
$ST = RT$ (Sides of an equilateral triangle)
$SP = PQ$ (Sides of square)
$\angle TSP = \angle TRQ$
Therefore, by SAS axiom,
$\triangle TSP \cong \triangle TQR$
This implies,
$PT = QT$ (CPCT)
Hence proved.
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