Q. 133.9( 19 Votes )
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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