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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.

Posted by Likhith Manohar Vadapalli 5 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years, 3 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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CBSE > Class 09 > Mathematics