Question

State true or false:

For the case of a parallelogram the bisectors of any two adjacent angles intersect at ${90}^0$.

• A. True
• B. False

Answer 1

The correct option is A True

Let $ABCD$ be the parallelogram

$\Rightarrow \angle A+\angle B=180°$

$\therefore \frac{1}{2}\angle A+\frac{1}{2}\angle B=90°$

In $△AOB$

$\Rightarrow \angle BOA+\angle ABO+\angle AOB=180°$

$\Rightarrow \frac{1}{2}\angle A+\frac{1}{2}\angle B+\angle AOB=180°$

$\therefore \angle AOB=180°-90°=90°$

$\therefore$ Angle bisects of $2$ adjacent angles intersect at $90°.$

Hence, the statement is true.