If a parallelogram has a right angle, is it a rectangle?

1 Answer
Dec 26, 2015

Yes, a parallelogram with a right angle has all right angles and is a rectangle.

Explanation:

In a parallelogram adjacent angles are supplementary, that is their sum is ${180}^{o}$. For proof refer to Unizor, menu items Geometry - Quadrangles - Parallelogram.

Therefore, adjacent angle to the one that is equal to ${90}^{o}$ is measured ${180}^{o} - {90}^{o} = {90}^{o}$, that is it's also right angle.
Since there are two adjacent angles, both are equal to ${90}^{o}$.

The remaining angle is opposite to a given, and opposite angles are equal in a parallelogram. So, it is also ${90}^{o}$.

So, all four angles are right angles and a parallelogram is a rectangle.