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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.

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.

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Answer 2

Aurora Ayala

No, a parallelogram with a right angle is not necessarily a rectangle. While a rectangle is a type of parallelogram with four right angles, a parallelogram with just one right angle does not meet all the criteria to be a rectangle. The other angles in a parallelogram with a right angle could be any measure, not necessarily 90 degrees, so it may not have all the properties of a rectangle.

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Answer from HIX Tutor

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