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Question

The quadrilateral(PQRS) formed by the bisectors of the angles of a parallelogram(ABCD) is a square.


A

True

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B

False

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Solution

The correct option is B

False


Given:
BCD is a parallelogram and AP, BR, CR, be are the bisectors of A,B,C and D, respectively.
We know that:
DC||AB and DA is a transversal.
A+D=180
[sum of cointerior angles of a parallelogram is 180]

12A+12=90

PAD+PDA=90

APD=90 [Sum of all angles of a triangle is 180]

SPQ=90 [vertically opposite angles]

Similarly, PQR=90

QRS=90

PSR=90

Thus, PQRS is a quadrilateral whose each angle is 90.

Hence, PQRS is a rectangle.


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