Question

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

Answer 1

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.