Given a quadrilateral \(PQRS\) in which the diagonal \( QS \) bisects each of the angles \( \angle PQR \) and \( \angle PSR \). Determine that:
(i) \(\Delta PQS \sim \Delta RQS\)
(ii) \(PQ=QR\)
Proof:
\(\angle PSQ =\) ()
\(\angle PQS =\) ()
Thus, \(\Delta PQS \sim \Delta RQS\) [by ].
Then corresponding sides are proportional to each other,
\(\frac{PQ}{QR}=\frac{QS}{QS}\)
\(\Rightarrow \frac{PQ}{QR}=1\)
\(\Rightarrow PQ = QR\).