Question

Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

Answer 1

Hint: We all know that if both the opposite sides are equal and parallel, then it will be a parallelogram. There is one more property of parallelogram that opposite angles are equal and we know that in rectangle all the angles are equal to $90^\circ $

Complete step-by-step answer:
So we know that the parallelogram must have opposite sides equal and parallel and also that the opposite angles must be equal then we can say that the given it is a parallelogram.
For example:
               

For $ABCD$ to be a parallelogram, anyone theorem must have to satisfy:
(1) $AD\parallel BC{\text{ and }}AB\parallel DC$
(2) $AD = BC,AB = DC$
(3) $\angle A = \angle C,\angle B = \angle D$
If anyone of the above three statements are equal then the quadrilateral is a parallelogram.
Now we know that in the rectangle, opposite sides are equal and all the angles are equal to $90^\circ $.
For example: $PQRS$ is a rectangle.
               

For rectangle:
$\angle P = \angle Q = \angle R = \angle S = 90^\circ $
All angles are equal to $90^\circ $.
So now we know that $\angle P{\text{ and }}\angle {\text{R}}$ are equal to $90^\circ $.
So we can say that $\angle P{\text{ and }}\angle {\text{R}}$ are equal.
We also know that $\angle Q{\text{ and }}\angle S$ are also equal to $90^\circ $.
So we can say that $\angle Q = \angle S$
So opposite angles are equal in rectangle so it is a parallelogram.

Note: It must be known that every square, rectangle are a parallelogram but every parallelogram may or may not be rectangle or square.