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.


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.