Question

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

Answer 1

Answer:

ABCD is a parallelogram

The adjacent angles of a parallelogram sum up to give 180

∘

i.e.,∠B+∠C=180

∘

2

∠B

+

2

∠C

=90

From ΔOBC⟹∠O=90

∘

⟹∠POR=90

∘

Similarly, all the 4 vetrices have right angles at their corners

Hence PQRS is rectangle.