Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. -Maths 9th

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. -Maths 9th
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Given Let ABCD be a parallelogram and AP, BR, CR, be are the bisectors of ∠A, ∠B, ∠C and ∠D, respectively. To prove Quadrilateral PQRS is a rectangle. Proof Since, ABCD is a parallelogram, then DC || AB and DA is a transversal. ∠A+∠D= 180° [sum of cointerior angles of a parallelogram is 180°] ⇒ 1/2 ∠A+  1/2 ∠D = 90° [dividing both sides by 2] ∠PAD + ∠PDA = 90° ∠APD = 90°    [since,sum of all angles of a triangle is 180°] ∴ ∠SPQ = 90°     [vertically opposite angles] ∠PQR = 90° ∠QRS = 90° and ∠PSR = 90° Thus, PQRS is a quadrilateral whose each angle is 90°. Hence, PQRS is a rectangle.
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