Difference between Parallelogram and a Rhombus

Parallelogram and rhombus are both types of quadrilaterals, which are polygons with four sides. While they share some similarities, there are distinct differences that set them apart. Understanding these differences can help in recognizing and distinguishing between the two shapes.

Definition and Basic Properties

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides are equal in length and opposite angles are equal in measure. The sum of the interior angles of a parallelogram is always 360 degrees.

On the other hand, a rhombus is a special type of parallelogram with all four sides equal in length. This property also implies that all angles of a rhombus are equal in measure. Like a parallelogram, the sum of the interior angles of a rhombus is 360 degrees.

Diagonals and Angles

One of the key differences between a parallelogram and a rhombus lies in their diagonals. In a parallelogram, the diagonals bisect each other, meaning they intersect at their midpoints. However, the diagonals of a rhombus not only bisect each other but also divide the angles into two equal parts. This property makes the diagonals of a rhombus perpendicular to each other.

Another difference is the angle measurements. In a parallelogram, the angles can vary, whereas in a rhombus, all angles are equal. This means that a rhombus has four right angles if it is a square, which is a special case of a rhombus.

Special Cases

It is important to note that a square is a special case of both a parallelogram and a rhombus. A square has all sides equal in length, making it a rhombus. Additionally, a square has all angles equal to 90 degrees, making it a special type of parallelogram.

Conclusion

In conclusion, the main difference between a parallelogram and a rhombus lies in their side lengths and angle measurements. A parallelogram has two pairs of parallel sides, while a rhombus has all four sides equal in length. The diagonals of a rhombus are perpendicular to each other, while those of a parallelogram bisect each other. Understanding these differences can help in identifying and classifying these shapes accurately.