Question

Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.​

Answer 1

Answer:

Given : ABCD a parallelogram

To Prove : PQRS is a rectangle 

DC∣∣AB and DA is a traversal 

∴∠A+∠D=1800

21∠A+21∠D=900

⇒∠SAD+∠SDA=900

∴∠ASD=900

∴ By concept of vertical angles

∠ASD=∠PSR=900

Simillarly we will get

∠PQR=∠QPS=∠QRS=900

∴PQRS is a rectangle

Step-by-step explanation:

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