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

Nov 16, 2015

Always.

#### Explanation:

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

#### Explanation:

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

DEFINITION of PARALLELOGRAM:
A quadrilateral (a polygon with 4 vertices) $A B C D$ with pairs of opposite sides parallel to each other (i.e. $A B$ is parallel to $C D$ and $B C$ is parallel to $A D$) is called a 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.