We explain the difference between rectangle and parallelogram with table. The rectangle and the parallelogram are quadrilaterals and two-dimensional shapes. Rectangles are a particular type of parallelogram. Even if it is a subtype, what makes the rectangle different from the parallelogram?
The area of quadrilaterals can be calculated using the formula (base) x (height). But an interesting fact is that the area can also be calculated
Rectangles are quadrilaterals that have four sides and opposite sides are equal. The four interior angles are equal and complementary to each other, that is, 90 degrees. With the Pythagorean theorem, we can calculate the sides of the rectangles. Common examples of things that are rectangular in shape are table tops, book covers, and laptop computers.
Parallelograms are also quadrilaterals that have four sides and with opposite sides are equal. The opposite sides are parallel to each other and hence the name. Opposite interior angles are equal and adjacent interior angles are supplementary.
the difference between the rectangle and the parallelogram is that although both opposite sides are parallel and equal, all angles of a rectangle are 90 degrees. Whereas for a parallelogram the opposite angles are equal and the adjacent angles are supplementary. If the interior angles of a parallelogram turned 90 degrees, it would give us a rectangle.
Comparison table between rectangle and parallelogram
Comparison rectangle parallelogram parameters
| Anglos | All angles are equal to 90 degrees. | Opposite interior angles are equal and adjacent angles are supplementary |
| Diagonal length | The lengths of the diagonal are equal | Diagonals differ in length. |
| Intersection angle | Diagonals intersect at right angles | The diagonals intersect so that the adjacent angles formed are supplementary |
| Symmetry | It has rotational and reflective symmetry. | It has a single degree of rotation of order 2 |
| Diagonal bisection | Diagonals bisect to form right triangles | Diagonals bisect to form isosceles triangles |
What is a rectangle?
Rectangles are special species of the parallelogram. Like a parallelogram, rectangles also have equal and parallel opposite sides. They have equal opposite interior angles and adjacent angles as supplementary.
Rectangles differ from parallelograms because all the interior angles of a rectangle are equal to 90 degrees. The diagonals are equal and even cross each other at the midpoint, forming right triangles.
The sides of a rectangle can be calculated if the values of the diagonals are known. This can be done according to the Pythagorean theorem since the triangles formed at the intersection of the diagonals have right angles.
Common examples of rectangles are books, cabinets, etc.
What is the parallelogram?
Parallelograms are quadrilaterals that have an order of symmetry equal to 2. They are called parallelograms because the opposite sides of these quadrilaterals are parallel, as in the case of a rectangle.
The opposite interior angles of a parallelogram are equal and the adjacent angles are supplementary, that is, the sum of the adjacent angles must equal 180 degrees. When the angles of the parallelogram are equal to 90 degrees, it forms a rectangle.
The diagonals of a parallelogram are not equal but bisect each other at the midpoints. The area of intersection forms an isosceles triangle.
Parallelograms follow the parallelogram law which states that the sum of the squares of the sides is equal to the sum of the squares of their diagonals. This law can be applied to find the sides of a parallelogram. India’s favorite sweet kaju katli is an example of a parallelogram.
Main differences between Rectangles and parallelograms
- The main difference between a rectangle and a parallelogram that makes the rectangle a special case of the parallelogram is the fact that all the angles in a rectangle are equal to 90 degrees. This is not the case in a parallelogram because the adjacent angles are only supplementary to each other.
- Although the diagonals cross each other at the midpoint, the diagonals of a rectangle are the same, but that is not true in the case of a parallelogram.
- The angle of intersection of the diagonals in the case of a rectangle is 90 degrees. But this is not necessary in the case of a parallelogram. Adjacent angles formed at the intersection are considered supplementary.
- The symmetry for both two-dimensional structures is different. This is because the symmetry of a rectangle can be taken from both its vertices and its sides. This means that a rectangle has rotational and reflective symmetry, unlike a parallelogram which only has rotational symmetry.
- Since the diagonals of a rectangle bisect at right angles, the area formed by the intersection is a right triangle. In the case of a parallelogram, the area formed under the intersection of the diagonals is an isosceles triangle.
Final Thought
If specific conditions apply to a parallelogram, it would form a rectangle. Therefore, a rectangle can be considered to be a special case of the parallelogram.
Parallelograms are quadrilaterals with equal and parallel opposite sides. This characteristic is what gave it the name “parallel.” The opposite angles of a parallelogram are equal and the adjacent angles are supplementary. To find the sides of a parallelogram, you can apply the parallelogram law.
A rectangle is a special case of parallelograms. If the adjacent and opposite angles of a parallelogram are equalized and the adjacent sides are made perpendicular to each other, a rectangle would be formed. Even if it is similar to the parallelogram, we can use the Pythagorean Theorem to find the sides of a parallelogram.
The opposite sides of a rectangle and a parallelogram are parallel to each other. But unlike the parallelogram, the adjacent sides of a rectangle are perpendicular to each other. This is because all the angles in a rectangle are equal to 90 degrees.
It is also seen that a rectangle is cyclical. This means that the points of a rectangle can be perfectly set within a circle without altering the structure. This cannot be done with the points that form a parallelogram.
