Question

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 1

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°

Answer 2

Hi,

Problem:PQRS is a parallelogram. T is the point of intersection of its diagonals.Write the answers of questions given below.

Solution:

(i) If l(PS) = 5.4 cm, then l(QR) = 5.4 cm

Reason: Property of parallelogram, that is opposite sides are equal,

here PQ = SR and SP = QR.

(ii) If l(TS) = 3.5 cm, then l(QS) = 7 cm

Reason: Since in a parallelogram diagonal bisect each other that means diagonal equally divides each other.

so if length of TS = 3.5 cm then length of TQ is = 3.5 cm

length of SQ = TS+TQ = 3.5+3.5 = 7 cm

(iii) If m∠QRS = 118°, find m∠QPS = 118°

Reason: In a parallelogram opposite angles are equal,so if ∠QRS = 118° then ∠QPS = 118°.

And sum of adjacent angles are 180°

(iv) If m∠SRP = 72°, then m∠RPQ = 72°

Reason: Since line PQ║ SR and Line PS║ RQ

so,∠SRP = 72° then ∠RPQ = 72°.

hope it helps you.