Question

.
prove that the quadrilateral formed by the
Bisectors of the angles of a parallelogram is a rectangle​

Answer 1

Answer:

Let P and Q be adjacent corners of a parallelogram, and let those angles have measure p and q. Let R be the point at which the angle bisectors at P and Q meet.

In △PQR, we have

180∘=∠R+∠RPQ+∠RQP=∠R+12p+12q=∠R+12(p+q)

Adjacent angles in a parallelogram are supplementary, so p+q=180∘. Thus,

180∘=∠R+90∘⟹∠R=90∘

which is to say: Adjacent angle bisectors in a parallelogram meet at right angles.