\(PQRS\) is a quadrilateral with sides \(PS\) and \(QR\) equal to each other. Also, the angles \(SPQ\) and \(PQR\) are equal to each other. Prove that \(\triangle PQS \cong \triangle PQR\).
Proof:
consider the triangles \(PQS\) and \(PQR\).
It is already given that \(PS = QR\).
Also, we know that \(\angle SPQ\) \(=\) \(\angle \).
is common to both \(\triangle PQS\) and \(\triangle PQR\).
Here, two pairs of corresponding sides and one pair of corresponding angles are equal.
Thus, by congruence rule, \triangle PQS \cong \triangle PQR\)
Since, \triangle PQS \cong \triangle PQR\), therefore by , \(\triangle PQS \cong \triangle PQR\).