Answer:
Step-by-step explanation:
(i)
PQRS is a parallelogram (given)
∴ QT = TS (Diagonals of a parallelogram bisects each other)
also, QT = RM (given)
∴TS = RM
PQRS is a parallelogram,
∴RT = PT (Diagonals of a parallelogram bisects each other)
also, SM = PT (given)
∴RT = SM
TS = RM
RT = SM
∴ RTSM is a parallelogram (both pairs of opposite sides are equal in length)
(ii)
QP // RS (Opposite sides of a parallelogram are parallel)
∴ ∡RQP = ∡NRS (Corresponding ∡s)
RTSM is a parallelogram(Proved above)
∴MS // RT (Opposite sides of a parallelogram are parallel)
∴NS//RP
∴∡RNS = ∡ QRP (Corresponding ∡s)
in ΔPQR and Δ NSR,
QP = RS (Opposite sides of a parallelogram are equal)
∡RQP = ∡NRS (Proved above)
∡RNS = ∡ QRP(Proved above)
∴ ΔPQR≡ΔSRN (AAS)
Corresponding sides of ≡ Δs are equal, ∴QR = RN
