Q. 133.9( 19 Votes )

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Answer :


Let ABCD is a parallelogram.


Since, DC||AB and DA is transversal.


A + D = 180


A + D = 90


PAD + PDA = 90


APD = 90


SPQ = 90


Similarly, PQR = 90, QRS = 90


And PSR = 90


Thus, PQRS is a quadrilateral each of whose angles is 90.


Hence, PQRS is a rectangle.


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