# Is a rectangle a parallelogram always, sometimes or never?

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Always.

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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*.

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#### Answer:

Any rectangle is a parallelogram

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

DEFINITION of PARALLELOGRAM:

A quadrilateral (a polygon with 4 vertices) *parallelogram*.

DEFINITION of RECTANGLE:

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.

NOTE:

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*.

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