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What is the quadrilateral formed by the angle bisectors of a parallelogram?(a) Square(b) Rectangle(c) Circle(d) RhombusI got this question in semester exam.This intriguing question comes from Properties of a Parallelogram in section Quadrilaterals of Mathematics – Class 9

Answer»

Correct CHOICE is (b) Rectangle

For explanation I would say: PQ || RS ⇒ ∠P + ∠S = 180°(Interior ANGLES on the same side of transversal)

⇒ ½ ∠P + ½ ∠S = ½ x 180°

⇒ ∠APS + ∠PSA = 90°——————-(i)

In ΔASP, ∠APS + ∠PSA + ∠SAP = 180°(Angle sum property of triangle)

⇒ 90° + ∠SAP = 180°(from equation i)

⇒ ∠SAP = 90°

⇒ ∠DAB = 90° (Vertically OPPOSITE angle)

Similarly, ∠ADB = 90°, ∠ABC = 90°, ∠DCB = 90°.

Hence, ABCD is a rectangle.


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