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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Updated on: 10-Oct-2022

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