Rectangle and parallelogram are both quadrilaterals and are 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 the quadrilaterals can be calculated by the formula (base)x(height). But an interesting fact is that the area can also be calculated.

**Rectangle vs Parallelogram**

**The main difference between the Rectangle and Parallelogram is that even though the opposite sides of both are parallel and equal, all the angles of a rectangle are 90 degrees. While for a parallelogram the opposite angles are equal and adjacent angles are supplementary.**

**If the internal angles of a parallelogram become 90 degrees, it would give us a rectangle.**

Rectangles are the quadrilaterals that have four sides, and the opposite sides being equal. All the four internal angles are equal and supplementary to each other i.e. 90 degrees.

With the Pythagoras theorem, we can calculate the sides of the rectangles. Common examples of things having a rectangular shape are table tops, book covers and laptops.

Parallelograms are also quadrilaterals that have four sides and with opposite sides are equal. The opposite sides are parallel to each other and thus the name.

The opposite internal angles are equal and the adjacent internal angles are supplementary.

## Comparison Table Between Rectangle and Parallelogram

Parameters of Comparison | Rectangle | Parallelogram |
---|---|---|

Angles | All the angles are equal to 90 degrees. | Opposite internal angles are equal and the adjacent angles are supplementary |

Length of diagonal | The lengths of the diagonal are equal | The diagonals differ in their length |

Angle of intersection | The diagonals intersect at a right angle | The diagonals intersect such that the adjacent angles formed are supplementary |

Symmetry | Has rotational and reflectional symmetry | Has an only rotational degree of order 2 |

Diagonal bisection | The diagonals bisect to form right-angled triangles | The 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 internal angles and have adjacent angles as supplementary.

Rectangles are differentiated from parallelograms because all the internal angles of a rectangle are equal to 90 degrees. The diagonals are equal and even intersect each other at the midpoint forming right-angles triangles.

The sides of a rectangle can be calculated if the values of the diagonals are known. This can be done according to the Pythagoras theorem since the triangles formed on the intersection of the diagonals are right-angled.

Common examples of rectangles are books, cupboards etc.

## What is Parallelogram?

Parallelograms are the quadrilaterals that have an order of symmetry as 2. They are called parallelograms because the opposite sides of these quadrilaterals are parallel, as in the case of a rectangle.

The opposite internal angles of a parallelogram are equal and the adjacent angles are supplementary i.e., the sum of the adjacent angles should be equal to 180 degrees. When the angles of the parallelogram equal to 90 degrees, it forms a rectangle.

The diagonals of a parallelogram are not equal but they bisect each other at the midpoints. The area of intersection forms an isosceles triangle.

The parallelograms follow the parallelogram law that 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 calculate the sides of a parallelogram.

Indiaโs favourite sweet *kaju katli* is an example of a parallelogram.

**Main Differences Between Rectangle and Parallelogram**

- The main difference between a rectangle and a parallelogram that makes rectangle a special case of the parallelogram is the fact that all the angles of 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.
- Even though the diagonals intersect each other at the midpoint, the diagonals of a rectangle are equal 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. The adjacent angles formed on intersection are seen to be supplementary.
- The symmetry for both the two-dimensional structures is different. This is because the symmetry of a rectangle can be taken from their vertices as well as their sides. This means a rectangle has both rotational and reflective symmetry, unlike a parallelogram that has only rotational symmetry.
- Since the diagonals of a rectangle bisect each other at a right angle, the area formed by the intersection is a right-angled triangle. In the case of a parallelogram, the area formed under the intersection of the diagonals is an isosceles triangle.

## Conclusion

If specific conditions are applied on a parallelogram, it would form a rectangle. Therefore, a rectangle can be considered to be a special case of the parallelogram.

Parallelograms are the quadrilaterals with opposite sides as equal and parallel. This feature is what gave it the name โParallelโogram.

The opposite angles of a parallelogram are equal and the adjacent angles are supplementary. To calculate the sides of a parallelogram, one can apply the Parallelogram Law.

A rectangle is a special case of the parallelograms. If the adjacent and opposite angles of a parallelogram are made equal and the adjacent sides are made perpendicular to each other, it would form a rectangle.

Even if it is similar to the parallelogram we can use the Pythagoras Theorem to calculate the sides of a parallelogram.

The opposite sides of a rectangle and a parallelogram are parallel to each other. But unlike parallelogram, the adjacent sides of a rectangle are perpendicular to each other.

This is because all the angles of a rectangle are equal to 90 degrees.

A rectangle is also seen to be cyclic. This means that the points of a rectangle can be fixed inside a circle perfectly without disturbing the structure.

This cannot be done with the points that make a parallelogram.

## References

- https://dl.acm.org/doi/pdf/10.1145/220279.220338
- https://www.tandfonline.com/doi/abs/10.1080/14794802.2014.933711

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