1.

PQRS is a parallelogram. T is the point of intersection of its diagonals.Write the answers of questions given below.(i) If l(PS) = 5.4 cm, then l(QR) = ?(ii) If l(TS) = 3.5 cm, then l(QS) = ?(iii) If m∠QRS = 118°, find m∠QPS.(iv) If m∠SRP = 72°, find m∠RPQ.

Answer»

If PQRS is a parallelogram , then
LENGTH of PQ = length of RS
length of PS = length of QR

(i) Given, length of PS = 5.4 cm
definitely , length of QR = 5.4 cm

(ii) if diagonals of PQRS parallelogram bisect each other at T
so, length of ST = length of TQ = length of QS/2
length of PT = length of TR = length of PR/2
here, Given , length of TS = 3.5 cm
so, length of QS = 2 × length of TS = 7cm

(iii)if PQRS is parallelogram then,
∠QRS = ∠QPS
and ∠PSR = ∠PQR
here, given, ∠QRS = 118°
so, ∠QPS = 118°

(iv) if PQRS is parallelogram ,
then, PQ || RS and PS || QR
so, ∠SRP = ∠RPQ
HENCE, ∠RPQ = ∠SRP = 72°


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