Parallelograms vs. Rectangle

Attribute	Parallelograms	Rectangle
Definition	A quadrilateral with opposite sides parallel	A quadrilateral with all angles at 90 degrees
Opposite sides	Equal in length and parallel	Equal in length and parallel
Diagonals	Do not necessarily bisect each other	Bisect each other and are equal in length
Angles	Opposite angles are equal	All angles are 90 degrees
Area	Base x Height	Length x Width

Definition and Properties

A parallelogram is a four-sided figure with opposite sides that are parallel and equal in length. It also has opposite angles that are equal. On the other hand, a rectangle is a special type of parallelogram with four right angles. This means that all angles in a rectangle are 90 degrees. Both shapes have four sides and four angles, but the key difference lies in the angles themselves.

Angles

In a parallelogram, the sum of the interior angles is always 360 degrees. This is because opposite angles are equal, and adjacent angles are supplementary. In contrast, a rectangle has four right angles, each measuring 90 degrees. This means that the sum of the interior angles in a rectangle is also 360 degrees. However, the key distinction is that all angles in a rectangle are right angles, while a parallelogram can have any combination of angles.

Sides

Both parallelograms and rectangles have opposite sides that are equal in length. This is a property of parallelograms, as their opposite sides are parallel and congruent. Rectangles, being a special type of parallelogram, also have this property. However, rectangles have the additional characteristic of having all four sides equal in length. This is not a requirement for parallelograms, as long as the opposite sides are equal and parallel.

Diagonals

Another key difference between parallelograms and rectangles lies in their diagonals. In a parallelogram, the diagonals bisect each other, meaning they intersect at their midpoints. This property holds true for all parallelograms, including rectangles. However, in a rectangle, the diagonals are equal in length and bisect each other at right angles. This is a unique property of rectangles that sets them apart from other parallelograms.

Area and Perimeter

The area of a parallelogram is calculated by multiplying the base by the height. This formula holds true for all parallelograms, including rectangles. However, in a rectangle, the base and height are the same, as the opposite sides are equal in length. This makes the area calculation simpler, as it is just the length of one side squared. Similarly, the perimeter of a rectangle is calculated by adding all four sides together, which are equal in length. In a parallelogram, the perimeter is the sum of all four sides, which may not be equal.

Applications

Parallelograms and rectangles are commonly used in various fields, such as architecture, engineering, and design. Parallelograms are often used to represent forces in physics and engineering, as they can be easily manipulated to show vectors and their components. Rectangles, on the other hand, are frequently used in construction and building design due to their right angles and equal sides. Both shapes have practical applications in real-world scenarios, making them essential geometric figures to understand.