Question

PQRS is a parallelogram in which angle R is equal to 90 degree prove that pqrs is a rectangle

Answer 1

As per the properties of parallelogram,
opp. angles are equal

therefore,

angle R = angle P = 90'

and adj. angles are complimentary,

therefore,

angle P + angle Q = 180'
angle Q = 90'

Now, angle S is opp. of angle Q, so they are equal.

angle S= angle Q = 90'

opp. sides of parallelogram are equal.
and as all the angles are pf 90'.

PQRS is a rectangle.