In the given figure, \( \mathrm{PQRS} \) is a quadrilateral and \( \mathrm{T} \) and \( U \) are...

In the given figure, \( \mathrm{PQRS} \) is a quadrilateral and \( \mathrm{T} \) and \( U \) are respectively points on PS and RS such that \( \mathrm{PQ}=\mathrm{RQ}, \angle \mathrm{PQT}=\angle \mathrm{RQU} \) and \( \angle \mathrm{TQS}=\angle \mathrm{UQS} \). Prove that \( \mathrm{QT}=\mathrm{QU} \).