Question

Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle. (Figure 5.24)

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:

Step-by-step explanation: