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

Always.

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

The properties of a rectangle are

The properties of a parallelogram are

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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Any rectangle is a parallelogram

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

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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A rectangle is always a parallelogram.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The endpoints of one diagonal of rhombus are (0,-8) and (8,-4). If the coordinates of the third vertex are (1,0). what are the coordinates of the forth vertex?
- What is the definition of an irregular quadrilateral?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 5 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #80 #, how long are the other two sides?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #72 #, what is the length of its longest diagonal?

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