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ABCD is a quadrilateral in which …

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ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively, show that the quadrilateral PQRS is a parallelogram.
  • 1 answers

Gaurav Seth 3 years, 11 months ago

 

Construction : Join AC

In DAC,

S and R are mid points of DA and DC respectively.

 By mid point theorem

SR || AC and SR =  ...(1)

Similarly in BAC,

PQ || AC and PQ =  ...(2)

From (1) and (2),

SR || PQ and SR = PQ

Hence PQRS is a parallelogram.

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