Question

prove that one angle of parallelogram is right angle then that quadrilateral is rectangle​

Answer 1

=>Let's ABCD be aparallelogram &m <C is 90°

Now,since ABCD is a parallelogram,then measure of angle will be equal to m<A which is

m<C =m<A=90°$\sf \pink{[Opposite \ angles \ of \ parallelogram \ are \ equal]}$

and m<A +m<B=180°$\sf \pink{[Corresponding \ Angles]}$

=>90° +m<B=180°

=>m<B =180°-90°

=>m<B=90°

________________

Also,m<B = m<D =90°$\sf \pink{[Opposite \ angles \ of \ parallelogram \ are \ equal]}$

Thus,

m<A = m<B =m<C =m<D=90°

Since,all the angles of the parallelogram are equal to 90°,therefore ABCD is a rectangle,by the properties of rectangle..

Hence proved✔