Question

PQRS is a parallelogram. T is the point of intersection of its diagonals. (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°, then m∠SPQ is _____​

Answer 1

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 x length of TS = 7cm

(iii)if PQRS is parallelogram then, ZQRS = ZQPS here, given, ZQRS = 118° so, ZQPS= 118°

and LPSR = <PQR

(iv) if PQRS is parallelogram, then, PQ II RS and PS II QR so, ZSRP = <RPQ

hence, ZRPQ = <SRP = 72°

Answer 2

Given:

PQRS is a parallelogram

T is the point of intersection of its diagonals

l(PS) = 5.4 cm , l(TS) = 3.5 cm , m∠QRS = 118°

Find :

l(QR) = l(QS) = m∠SPQ = ?

Solution:

(1) If l(PS) = 5.4 cm, then l(QR) = ?

• We know that opposite of parallelogram are congruent
• l(PS) = l(SR)

∴ l(PS) = 5.4 cm then  l(QR) = 5.4 cm

(2)  If l(TS) = 3.5 cm, then l(QS) = ?

• Diagonals of parallelogram bisect each other

• l(QS) = 2 × l(TS)

• l(QS) = 2 × 3.5

• l(QS) = 12.25 cm

∴ If l(TS) = 3.5 cm, then l(QS) = 12.25 cm

(3)  If m ∠QRS = 118°, then m ∠SPQ = ?

• Opposite angles of parallelogram are congruent

• m ∠QRS = m ∠SPQ

∴So If m ∠QRS = 118°, then m ∠SPQ =  118°

Hence the answer are as follows:

(1) l(PS) = 5.4 cm then  l(QR) = 5.4 cm

(2) If l(TS) = 3.5 cm, then l(QS) = 12.25 cm

(2) If m ∠QRS = 118°, then m ∠SPQ =  118°