Is a rectangle a parallelogram always, sometimes or never?

2 Answers
Nov 16, 2015




For this question, all you need to know are the properties of each shape.

The properties of a rectangle are

  • 4 right angles
  • 4 sides (Polygonal)
  • 2 pairs of opposite congruent sides
  • congruent diagonals
  • 2 sets parallel sides
  • mutually bisecting diagonals

The properties of a parallelogram are

  • 4 sides
  • 2 pairs opposite congruent sides
  • 2 sets of parallel sides
  • both pairs opposite angles are congruent
  • mutually bisecting diagonals

Since the question is asking if a rectangle is a parallelogram, you would check to make sure all the properties of the parallelogram agree with those of a rectangle and since they all do, the answer is always.

Nov 20, 2015


Any rectangle is a parallelogram


We have to start with definitions of a parallelogram and a rectangle.

A quadrilateral (a polygon with 4 vertices) #ABCD# with pairs of opposite sides parallel to each other (i.e. #AB# is parallel to #CD# and #BC# is parallel to #AD#) is called a parallelogram.

A parallelogram with all 4 interior angles congruent to each other is called a rectangle.

So, straight from a definition we see that any rectangle is a parallelogram with additional property of having all interior angle congruent to each other.

There are different definitions of a rectangle, all equivalent to each other. In some cases the definition does not explicitly include the fact that it is, firstly, a parallelogram. Instead, the definition might specify that there are four sides and all interior angle are right angles. But, whatever the definition is, from it immediately follows that any rectangle is a parallelogram. If you find such a definition, an easy proof will be sufficient to show that a rectangle is a parallelogram.