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Difference Between Parallelogram and Quadrilateral
In geometry, a quadrilateral is a polygon with four sides, while a parallelogram is a special type of quadrilateral with some specific properties that differentiate it from other quadrilaterals.
What is Parallelogram?
A parallelogram is a specific type of quadrilateral that has two pairs of parallel sides. In other words, the opposite sides of a parallelogram are parallel and congruent, meaning they have the same length. Parallelograms also have opposite angles that are congruent, meaning they have the same measure.
Properties of Parallelogram
One of the most important properties of a parallelogram is that the opposite sides are parallel. This means that if you extend one side of a parallelogram, it will never intersect the opposite side. Additionally, the opposite sides of a parallelogram have the same length, which means that they are congruent.
Another important property of a parallelogram is that the opposite angles are congruent. This means that if you measure one angle of a parallelogram, and then measure the angle across from it, you will get the same measure. This property is known as the alternate interior angles theorem.
Moreover, parallelograms have two pairs of congruent adjacent angles, meaning they have the same measure and share a side. The sum of adjacent angles in a parallelogram is 180 degrees.
What is Quadrilateral?
A quadrilateral is a two-dimensional geometrical structure that always has four sides and four corners. A quadrilateral is also frequently called a polygon that has four sides. The part of the term “quad” means four.
Properties of Quadrilateral
There are many different types of quadrilaterals that can be found. Each of these quadrilaterals has their own specific set of properties that further characterize and define the shape.
The sum of all the angles that are found inside (interior) of a simple quadrilateral all adds up to 360 degrees.
Opposite sides may or may not be equal in length depending on what type of quadrilateral we are concerned with. A square, for instance, would have sides that are all the same length, but a rectangle would not. Similarly, opposite sides of the quadrilateral may or may not be parallel.
A rectangle, rhombus and square all have parallel opposite sides, but a kite does not have any opposite parallel sides at all. In fact, all parallelograms can also be characterized as being types of quadrilateral shapes.
Some quadrilaterals are called complex structures because the sides cross over to form unusual shapes.
Types of Quadrilaterals
There are several geometric shapes that can be classified as types of quadrilaterals. In fact, all parallelograms are also classified as being quadrilaterals since they have four sides. This means that a rhombus, square and rectangle are quadrilaterals. In addition to these shapes, a trapezoid and kite are also types of quadrilaterals.
Examples from the Real World
There are several examples of quadrilaterals from everyday life. A square table or a rectangular wall of a house, are shapes that are quadrilateral. A kite that somebody flies is also a quadrilateral. There are many more examples of quadrilaterals than there are of parallelograms because the opposite sides do not need to be parallel. The shape simply has to have four corners and four sides.
Differences: Parallelogram and Quadrilateral
The following table highlights the major differences between a Parallelogram and a Quadrilateral −
Characteristics |
Parallelogram |
Quadrilateral |
---|---|---|
Definition |
A parallelogram is a two-dimensional geometric structure that always has four sides, of which opposite sides are the same length, and parallel. |
A quadrilateral is simply a two-dimensional structure that has four sides to it. |
Parallel sides |
In a parallelogram there is always a pair of sides that are opposite that are parallel. |
In a quadrilateral, there are only sometimes parallel sides present, and at other times opposite sides are never parallel. |
Opposite sides of equal length |
A shape that is a parallelogram always has opposite sides that are of the same length. |
A shape that is a quadrilateral does not always have sets of opposite sides that are of the same length, sometimes they are not equal length. |
Opposite angles of equal size |
A parallelogram is a shape in which the opposite angles are always of equal size. |
A quadrilateral is a shape in which the opposite angles are sometimes, but not always of equal size. |
Types |
The following geometric shapes are all also classified as being types of parallelograms: square, rhombus, and rectangle. |
Geometric shapes that can be classified as being quadrilaterals include the square, rectangle, rhombus, trapezoid, kite and an assortment of complex shapes. |
Conclusion
In conclusion, a parallelogram is a specific type of quadrilateral with two pairs of parallel sides and opposite angles that are congruent. Other types of quadrilaterals, such as rectangles, squares, rhombuses, trapezoids, and kites, have different properties and do not necessarily have parallel sides or congruent opposite angles.
Understanding the differences between these various types of quadrilaterals can be helpful in solving geometry problems and understanding the properties of different shapes.