Introduction
Geometry is one of the important branches of mathematics. And, shapes are the base of geometry. Both a kite and a rhombus are a significant part of geometry. A kite is a diamond-shaped shape in which two adjacent sides are equal. One of the opposite angles is equal. And, one diagonal divides the kite into two isosceles triangles and the other divides it into two congruent triangles. The subset of a kite is a rhombus. However, being rhombus a part of a kite, it inherits all the features of a kite. Also, its significant properties include equal adjacent sides, etc.
Kite vs. Rhombus
A Kite is shaped like a kite that flies in the sky. The very name of the kite is derived from the resemblance in the shape of a kite and a flying kite. The specific characteristics of a kite are that its two adjacent sides are equal. It is different from a parallelogram that has opposite sides equal. One of the pairs of angles is equal. The diagonals of a kite divide it into two equal parts. One makes a congruent pair and the other makes an isosceles triangle.
A kite looks like a slice of a diamond. The upper side of a kite is slightly smaller and the tail is slightly longer. This gives the advanced feature to give a defined look to the shape.
A rhombus is the same as a kite. The only difference is that in a rhombus, all adjacent sides are equal. It means all sides of a rhombus are equal. And, the opposite angles of the rhombus are equal. The diagonals bisect each other at 90°.
A rhombus is a subset of both a parallelogram and a kite. Thus, it carries out all properties of a parallelogram. For example, opposite sides are parallel and equal to each other, diagonals bisect each other, adjacent sides are equal, the sum of two consecutive angles is 180°, etc. It also has features of a kite. Adjacent sides are equal, diagonals bisect other perpendicularly, etc.
Difference Between Kite and Rhombus in Tabular Form
| Parameter of comparison | Kite | Rhombus |
| Shape | Flying kite-shaped | Diamond of a card-shaped |
| Length of sides | Two adjacent angles are equal | All adjacent angles are equal |
| Subset of | Quadrilateral | Kite and parallelogram |
| Parallel | Opposite sides are not parallel | Opposite sides are parallel |
| Area | (P.h)/2 | (P.q)/2 |
| Set of | A rhombus | A square |
| Axis of symmetry | 1 | 2 |
What is a kite?
A kite is a quadrilateral with four sides in which adjacent are equal in length. The name ‘kite’ is given based on its shape. It resembles a flying kite. The other name for kite is deltoids but it is not popular among people.
A kite is quite specific in its shape. It has four sides with equal adjacent sides. A parallelogram also has 4 sides but the equal sides are opposite not adjacent. One of the two opposite angles of the quadrilateral is equal. A kite is a part of Euclidian geometry but is not normally used.
Features of a kite
There are certain features of a kite. These are
- A kite should have two pairs of equal sides that are located adjacent to each other.
- Its diagonals should bisect each other perpendicularly.
- One of the diagonals bisects the two opposite angles
- One of the diagonal divide the kite into two congruent triangles and the other divides the kite into two isosceles triangles.
- One of the diagonals is the line of symmetry of the kite. That is, it divides the whole kite into two equal parts.
Symmetry
A kite has an axis of symmetry. There could be only two non-self crossing quadrilaterals that can have a single axis of symmetry. The first is, isosceles trapezoids and the other is a kite. Other forms of kites have more than one axis of symmetry. One axis of symmetry symbolizes that a kite can be divided into two equal parts. The line of symmetry passes through one of the diagonals of the kite. Another diagonal divides the kite into two isosceles triangles.
For example, a part of a kite, the rhombus has two axes of symmetry whereas the square has four axes of symmetry.
Hierarchy
There are two types of hierarchy that are followed in the differentiation of shapes. One is, hierarchical in which shapes are divided into sets and subsets. For example, kite and parallelogram are the hierarchy of quadrilateral. Next is, partitional in which shapes are not divided into sets and subsets.
A kite is a hierarchical geometry. Other shapes like rhombus are considered as the subset of a kite. Because it has fulfilled all criteria of a kite. However, a rhombus has four equal sides and diagonals. Also, it has two axes of symmetry.
Next is, the square. It is considered as a hierarchy of a rhombus. The only difference is that it has four equal angles as well. Since square is also a hierarchy of a rhombus, hence it is indirectly a hierarchy of the kite.
Types of kites
According to Euclidean geometry, a kite can be classified into two types.
First is, the equilateral kite. The kite in which all sides are equal. The specific name of this kite is a rhombus. In a rhombus, all sides are equal but not angles.
The second is an equiangular kite. A kite that has four equal angles is known as an equiangular kite. Rectangular and square are two equiangular kites. All the angles of a square are 90°.
Area
The area of a kite is recorded via the method of calculation of orthodiagonal quadrilateral. And, the area is half of the product of the perpendicular and the height of the quadrilateral.
A= (P*H)/2
Where,
A= area
P= perpendicular
H= height
A kite is both concave and convex. Mostly, a convex kite is used. In fact, the kite has become the synonym of a convex kite. The concave kite is sometimes known as dart or arrowhead.
What is a rhombus?
A Rhombus is a hierarchical a version of a kite. However, when it is seen through partitional division, a rhombus is not a subset of any other shape. A rhombus is a quadrilateral in which adjacent sides are equal. It is also known as equilateral quadrilateral because it has four equal lines.
A rhombus is a special case of a kite and a parallelogram. A kite has two adjacent sides equal and a parallelogram has two opposite sides equal. A rhombus is a combination of these two because it has both adjacent and opposite sides equal. However, a rhombus is not an equiangular shape because the angles of the rhombus are not equal. Only opposite angles of a rhombus are equal.
Features of a rhombus
Characteristic is an important part of a person, place or thing. A rhombus also has some characteristics that define it. A quadrilateral can be a rhombus only when it fulfils certain conditions
- Diagonals of a rhombus intersect each other at the right angle.
- Two diagonals are angular bisectors of all the angles of a triangle.
- The four sides of the rhombus are equal in length and two opposite angles are equal
- Two ddiagonals of a rhombus bisect each other. It means diagonals are perpendicular bisectors of each other.
- Diagonals bisect the rhombus in two congruent triangles.
A rhombus can inscribe a circle in it in which all four sides of the rhombus issue tangent of the circle. That’s why a rhombus is called a tangential quadrilateral. And, all tangents are equal in size.
Hierarchy
A rhombus is a parallelogram. It has all properties that a parallelogram must-have. A parallelogram should have two parallel lines. A rhombus has two equal and opposite parallel lines. A parallelogram should have diagonals bisecting each other. Diagonals of a rhombus bisect each other at 90°.
The subsets of a rhombus are square. In the square, all angles are equal to 90°. It has equal opposite angles and adjacent sides are equal in length. The only criteria for a rhombus to become a square are that the angle must be 90°.
Since a rhombus is a subset of a parallelogram and a kite. And, a square is a subset of a rhombus. Thus, indirectly square is also a subset of a parallelogram. It has all features of a kite as well as a rhombus.
However, when it is seen through partitional division, the square is not a subset of any other set. It is independent in itself. Square is an independent identity in itself.
Characterization
A rhombus is also a parallelogram. Thus, it carries all properties of a parallelogram. The diagonals bisect each other.
Thus, the relation between the diagonals and sides of the rhombus when diagonals are p and q, and sides are a.
4a²= p² + q²
Now, let us consider the longer diagonal to be p and the shorter diagonal to be q, then the formulas of both the diagonals are
P= a+ √(2 + 2cos b)
Q= a+ √(2-2cos b)
Area
In a parallelogram, the area is calculated by multiplying the height and the base of the parallelogram. Similarly, in the rhombus, the area is calculated by the height and the base of the rhombus.
Let the sides of the triangle are base and the height of the triangle be h,
Then,
Area of the rhombus= k= a.h
If the area is calculated diagonally, then the area would be,
Area= (p.q)/2
Difference Between a Kite and a Rhombus in Points
- A Kite had two adjacent sides equal. The two adjacent sides in the upper part of the kite are smaller and the lower part is a little longer. The definite shape of the kite looks like the kite that we fly. However, a rhombus has all adjacent sides equal. All four sides of the rhombus are equal in length.
- The number of axis of symmetry in a kite is one. Only two figures have one axis of symmetry. One is a kite and the other is a trapezoids quadrilateral. However, a rhombus has two axes of symmetry like a parallelogram.
- A kite is a subset of a quadrilateral. In other words, a kite is a unique figure in itself. Also, it has all properties of a quadrilateral. For example, the sum of angles of a quadrilateral is 360°. While a rhombus is a subset of a kite and a parallelogram. And, it carries all features of a kite and a parallelogram.
- A kite doesn’t have any parallel lines. However, a rhombus has two parallel lines and parallel lines are opposite each other like a parallelogram. The only difference is that a parallelogram has only opposite sides equal. But a rhombus has all sides equal.
- A kite is a set of rhombus. It means a rhombus has all features that a kite has. However, the subset of a rhombus is a square. It means a square carries all features of a rhombus.
- The area of a kite, let p be one of the diagonal and h be the height. Then, the area of a rhombus is (p.h)/2. However, let p and q be the diagonals of a rhombus. Then, the area of the rhombus is, A= (p.q)/2.
Conclusion
A kite is a shape on which two adjacent sides are equal. Its diagonal bisect each other at a right angle and the opposite angles. Its diagonals divide the shape one into two isosceles triangles and the other in congruent triangles. The adjacent sides of the kite are equal.
A rhombus is just a modified version of a kite. The only change is that all adjacent sides are equal. This makes the rhombus a regular polygon. Also, its diagonals bisect each other at the right angle. However, the method of calculation of area is different in both of them. Being diagonals the height and base of the rhombus, the area can easily be calculated by dividing the multiple of the base and the height by two.
A rhombus is also a modified version of a parallelogram. The only difference is that all sides of a rhombus are equal in length.
References
- https://en.m.wikipedia.org/wiki/Rhombus#:~:text=In%20plane%20Euclidean%20geometry%2C%20a,sides%20are%20equal%20in%20length.
- https://en.m.wikipedia.org/wiki/Kite_(geometry)
