Question

If one angle of a parallelogram is a right angle, then prove that it is a rectangle.

Answer 1

ABCD is parallelogram
$\therefore AB||CD$ & $AD||BC$ of $\angle A={90}^o$
then, $\angle D={180}^o-{90}^o={90}^o$
& $\angle D=\angle B$ & $\angle A=\angle C$
(opposite angle of parallelogram are equal & sum of adjacent angle of parallelogram $={180}^o$)
$\therefore \angle A=\angle B=\angle C=\angle D={90}^o$
It is a rectangle.