Smaller diagonal QS of a parallelogram PQRS is perpendicular to the sides PQ and RS. prove that PR2-QS2=4PQ2


Consider right angled ΔPQM.
QM2 + PQ2 = PM2....(Pythagoras theorem)
But PM = 1/2 PR and QM = 1/2 QS.....(diagonals of a paralleogram bisect each other )
Hence (1/2 QS)2 + PQ2 = (1/2PR2)
i.e. 4PQ2 + QS2 = PR2
i.e. PR2 - QS2 = 4PQ2
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