Question

State true or false:

The bisectors of angles B and C of a parallelogram ABCD meet at point O. If triangle OBC formed is an isosceles right-angled triangle, then the quadrilateral ABCD is a rectangle.

• A. True
• B. False

Answer 1

The correct option is A True

$OB$ bisects $\angle B$ and $OC$ bisects $\angle C$
Given: $\angle OBC=\angle OCB$ isosceles right-angled triangle
$2\angle OBC=2\angle OCB$
$\angle B=\angle C$
Given, $ABCD$ is a parallelogram
Thus, $\angle B+\angle C=180$
$2\angle B=180$
$\angle B={90}^{\circ }$
Hence, $\angle B=\angle C={90}^{\circ }$
Thus, $ABCD$ is a rectangle.