A common question you always come across when dealing with geometry and shapes is, “Why is a rectangle always a parallelogram, but a parallelogram is not always a rectangle?”
A rectangle is always considered a parallelogram because of its features. These include the pair of supplementary co-interior angles, and all interior angles are congruent with the four right angles.
Two right angles add to a straight line which means that the opposite sides of a rectangle are parallel.
Thus when the opposite angles are equal and parallel, a rectangle is automatically considered a parallelogram.
A parallelogram cannot be called a rectangle, however, because of the multiple features that differ, especially with the congruent angles being equal and perpendicular in the case of a rectangle.
Rectangles and parallelograms are among the most common shapes you will likely come across in learning and interacting with geometry.
The two are distinct features and may mistakenly be perceived as the same. Yes, they do hold some similarities, but there are distinct differences.
This article sheds light on the differences and the similarities and differences between a rectangle and a parallelogram.
Learning this can help you improve your solving capability in geometry and shapes. A standard definition for the two is as follows:
Rectangle: It refers to a two-dimensional shape with four equal interior angles and vertices, thus a quadrilateral—all the four adjacent angles of a rectangle measure 90 degrees.
A rectangle is also regarded as a parallelogram because it has equal and parallel opposite sides.
Parallelogram: It is also a two-dimensional shape with four vertices. The interior angles are formed at the vertices in a way that adjacent angles may add up to make supplementary angles.
If the properties are parallel and congruent, it is considered a quadrilateral.
Why is a parallelogram not a rectangle?
A parallelogram’s main features involve opposite sides that are equal and parallel. Thus this means that they can be in different angles and consist of varied angles.
A rectangle, however, has definite features that focus on the sides of the rectangles, which are 90 degrees or right angles.
A parallelogram’s angles are very different compared to a rectangle. Thus with the definite features of the rectangle like the angles, a parallelogram cannot be a rectangle.
A parallelogram has a chance of being variant in very many angles and lengths. These differences involve common features that make a parallelogram not fit into a rectangle.
Another feature that makes a parallelogram different and does not fit into a rectangle is the unequal diagonals.
The diagonals of a parallelogram are not equal in length, especially with the variety of angles and length.
This, however, is very different from the features that make up a rectangle which involves equal length to its diagonals.
The nature of a rectangle gives the equal length of the diagonals on the rectangle. Despite both being quadrilaterals, meaning they have four sides, they have different properties which can distinctly identify them.
Why is a rectangle always a parallelogram?
Judging from the description of what a parallelogram is, a rectangle automatically fits in as one. A parallelogram’s features are clear and cover many features that define the rectangle.
The most common is the equal and parallel angles. A rectangle has four sides which are all right angles and thus congruent.
These angles being parallel to each other and equal, qualify for a parallelogram. The description or features link the rectangle always to be considered a parallelogram.
The two properties cover other quadrilaterals and thus accommodate even other various lengths.
The features of a rectangle are specific and do not change over time which is also different from the parallelogram.
Another feature is how the diagonals always dissect each other; diagonals in a rectangle are equal and dissect each other in the middle.
In a parallelogram, its diagonals also dissect each other, thus, making a rectangle valid to be considered a parallelogram.
A parallelogram covers varied forms of other quadrilaterals like the rhombus, which is different from a rectangle.
Thus, it explains why a rectangle is always a parallelogram, but a parallelogram is not. Despite the rectangle being limited to distinct properties, it still makes it a parallelogram.
How is a rectangle different from a parallelogram?
The difference is mainly witnessed in the opposite sides, wherein in a parallelogram, the opposite sides are equal; in the sides in a rectangle, the opposite sides are equal and perpendicular to each other.
The right-angle nature of a rectangle distinguishes it from the parallelogram, whose sides may not be perpendicular to each other.
The same side angles in a rectangle and parallelogram supplement each other, but for a rectangle, they are distinctly at a right angle; in a parallelogram, the sides supplement each other but have varied angles with which they are identified.
Diagonals in a parallelogram are unequal, while those in a rectangle are equal. This is another difference brought about by the nature of the quadrilaterals.
The equal angles and sides in a rectangle present equal diagonals. On the other hand, parallelograms may include different sizes in terms of angles, which then bring unequal diagonals.
However, the diagonals bisect each other. These differences may not be hard to notice; however, you must clearly understand the representations to help you not mix the two.
Therefore, in highlighting the differences, the focus is felt on the opposite sides, which are not always equal, and also the diagonals which may serve as a better indicator of the obvious differences.
What do all rectangles and parallelograms have in common?
It is no doubt that rectangles and parallelograms share so much in representation. Identifying these differences is key to solving and understanding how you achieve solutions in geometry.
However, it is also essential to highlight the features common to both rectangles and parallelograms for an efficient understanding of the problems and features. Some of the common similarities would include:
They are both quadrilaterals. A quadrilateral is a shape representing four sides; thus, they all fit into the description.
- The opposite sides are parallel to each other.
- Opposite angles for both are also equal. The sum of all the interior angles amounts to 360 degrees.
- The diagonals for a rectangle and a parallelogram bisect each other. Here, although the differences are discussed in the diagonals, they all bisect each other.
- The adjacent angles for both are supplementary to each other. They all amount to 180 degrees.
- The opposite sides of the two quadrilaterals are of equal length.
These are essential tips to learn and help you understand their shapes’ differences. In figuring out the differences and similarities, it becomes easier for you to navigate the questions and calculations to give accurate results.
It can be easy to mix up the two, especially with the similarities between opposite and equal angles and sides.
Thus, it becomes important to understand the differences and take a keen insight into the distinctive angles in the case of a rectangle.
However, the similarities also make it clear that the different geometrical shapes are all related and thus hold identical properties or characteristics.
In learning and familiarizing yourself with the shapes, the discussed work can act as basics to fully immerse you in learning the differences and help you achieve intended solutions for your work at all times.