Question

Prove that in a parallelogram, the angle framed by the angles bisector of two adjacent angles is a right angle.

Answer 1

R.E.F image

$ABCD$ is a parallelogram

we have to prove

$\angle AOD={90}^{\circ }$

$\angle DAB+\angle ADC={180}^{\circ }$

$\frac{1}{2}\angle DAB+\frac{1}{2}\angle ADC={90}^{\circ }$

$\frac{1}{2}(\angle DAB+\angle ADC)={90}^{\circ }$

$\angle 1+\angle 2={90}^{\circ }$

$\angle DAO+\angle ODA={90}^{\circ }$

In $\Delta ODA$

$\angle 1+\angle 2+\angle DOA={180}^{\circ }$

${90}^{\circ }+\angle DOA={180}^{\circ }$

$\angle DOA={90}^{\circ }$

$\therefore \angle AOD={90}^{\circ }$