Question

Prove that the bisectors of a parallelogram form a rectangle

Answer 1

Heya,

》Prove that the bisectors of a parallelogram form a rectangle

GIVEN:-
ABCD is a parallelogram in which each angle is bisected.

TO PROVE:-
PQRS is a rectangle.

PROOF:-

∠"A" + ∠"D"=180 deg.

1/2 ∠"A" + 1/2 ∠"D" = 180/2 [divide the both sides with 2]

Therefore,

∠1+ ∠2 = 90deg.

In triangle ADP
( ∠1+ ∠2)+ ∠3=180 deg.
90+ ∠3=180 deg.

Hence,

∠3= 180-90
∠3= 90

Therefore,
∠4= 90 [Vertically opposite angles]

Similarly ∠P= ∠Q= ∠R= ∠S=90deg.

So, PQRS is a parallelogram[opposite angle are equal]

As one of the angle is 90deg PQRS is a rectangle.

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Hope my answer helps you :)

Regards,
Shobana