In Fig., \(OP = OQ\) and \(OS = OR\). Prove that
(i) \(∆ POS ≅ ∆ QOR\) and
(ii) \(PS || QR\)
Proof:
(i) In \(∆ POS\) and \(∆ QOR\),
\(OP = OQ\) [Given]
\(OS = OR\) [Given]
\(\angle POS = \angle\) ( )
Thus, \(∆ POS ≅ ∆ QOR\) (by the congruence rule),
Hence proved
(ii) In \(\triangle POS\) and \(\triangle QOR\), we have:
\(∠ OPS = ∠ OQR\) []
Therefore, \(PS \parallel QR\).
Hence, we proved.