Is a rectangle a parallelogram always, sometimes or never?

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.

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.

A rectangle is always a parallelogram.