Q13 of 56 Page 82

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


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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