Two triangles \(\triangle PSQ\) and \(\triangle QRS\) are formed on the same base. \(PQ = PS\), and \(SR = QR\). Prove that \(\angle PQR = \angle PSR\).
Proof:
Let us consider the triangles \(PQR\) and \(PSR\).
We already know that \(PQ =\), and \(SR = \).
Also, is common to both \(\triangle PQR\) and \(\triangle PSR\).
Thus, all three corresponding sides of triangles \(PQR\) and \(PSR\) are equal.
Hence by congruence criterion, \(\triangle PQR\) and \(\triangle PSR\) are congruent to each other.
That is, \(\triangle PQR \cong \triangle PSR.\)
Thus by Corresponding Parts of Congruent Triangles (CPCT), the \(\angle PQR = \angle PSR\).