Question

ABCD is a trapezium in which AB || DC and AD = BC. If P, Q, R and S be respectively the mid-points of BA, BD, CD and CA, then PQRS is a

(a) Rhombus 

(b) Rectangle 

(c) Parallelogram 

(d) Square

Answer 1

(a) Rhombus.

In ΔBDC, Q and R are the mid-points of BD and CD respectively.

∴ QR || BC and QR = \(\frac12\) BC

Similarly, in ΔABC, PS || BC and PS = \(\frac12\) BC =

∴ PS = QR 

Also in ΔABD, PQ || AD and PQ = \(\frac12\) AD

In ΔADC, SR || AD and SR = \(\frac12\) AD = 

∴ PQ = SR 

AD = BC ⇒ PS = QR = PQ = SR ⇒ PQRS is a rhombus.