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In the adjoining figure, $P R=S Q$ and $S R=P Q$.
a) Prove that $\angle P=\angle S$.
b) $\Delta SOQ \cong \Delta POR$.
Given :
$PR = SQ$
$SR = PQ$
To do :
We have to prove that, a) Prove that $\angle P=\angle S$ and b) $\Delta SOQ \cong \Delta POR$.
Solution :
(a)
In $△SQR$ and $△PQR$,
$PR = SQ$ (Given)
$SR = PQ$ (Given)
$QR = QR$ (Common side)
Therefore, by SSS congruence,
$△SQR ≅ △PQR$.
$∠QSR = ∠RPQ$ (CPCT)
Therefore,
$∠P = ∠S$
Hence Proved.
(b)
In $△SOQ$ and $△POR$,
$SQ = PR$ (Given)
$∠QSO = ∠RPO$ (from a)
$∠SOQ = ∠POR$ (Vertically opposite angles)
Therefore, by AAS congruence,
$△SOQ ≅ △POR$.
Hence Proved.
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