Question

the quadrilateral formed by the intersection of the angel bisectors of a parallelogram is a ​

Answer 1

Given,

Let ABCD be a parallelogram  

To prove Quadrilateral PQRS is a rectangle.

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]

∠SAD + ∠SDA = 90°

∠ASD = 90°    [since,sum of all angles of a triangle is 180°]

∴ ∠PSR = 90° and ∠PQR = 90°     [vertically opposite angles]

∠QRS = 90°and ∠QPS = 90° [vertically opposite angles]

So, PQRS is a quadrilateral whose each angle is 90°.

Hence, PQRS is a rectangle.

Answer 2

Answer:

Rectangle

Step-by-step explanation:

As all the four angles of the quadrilateral are right angles, we can conclude that it is a rectangle.

So,The quadrilateral formed by the intersection of the angle bisectors of a parallelogram is a Rectangle

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