Given: AD = BC
P, Q, R and S are the midpoints of AB, AC, CD and BD respectively.
So in ∆ABC, if P and Q are midpoints of AB and A respectively ⇒ PQ ∥ BC
And PQ = (1/2)BC …(i)
Similarly in ∆ADC,
QR = (1/2)AD …(ii)
SR = (1/2)BC …(iii)
PS = (1/2)AD = (1/2)BC [∵ AD = BC]
Using equations (i), (ii), (iii) & (iv), we get
PQ = QR = SR = PS
All these sides are equal.
⇒ PQRS is a rhombus.
Hence, shown that PQRS is a rhombus.
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