If ΔPQT≅ΔRSQ, using RHS criterion, then
∠TQP = ∠SQR
PQ = RS
PQ = RQ
PT = RS
In two congruent triangles, corresponding parts (sides/angles) are equal. So, the corresponding sides for ΔPQT≅ΔRSQ are PQ=RS or PT=RQ.
In isosceles ΔPQR, PQ = QR, M is the mid point of QR. LM ⊥ PQ, MN ⊥ PR. By which criterion of congruency is ΔQLM ≅ ΔMNR.