We want to state whether a parallelogram is always, sometimes, or never a rectangle. To do so, we will compare the definitions of a rectangle and a parallelogram.
A parallelogram is a quadrilateral with two pairs of parallel and congruent sides.
As we can see, a parallelogram does not have to have four right angles. Therefore, it is not always a rectangle. Let's take a look at an example parallelogram that is not a rectangle.
This parallelogram does not have four right angles, so it is not a rectangle. However, some parallelograms can have four right angles — in which case, they are considered rectangles. Let's take a look at an example of a parallelogram that is also a rectangle.
The quadrilateral has two pairs of parallel and congruent sides and four right angles. This means that it is both a rectangle and a parallelogram. Therefore, a parallelogram is sometimes a rectangle.
