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Symmetry Formula

The word symmetry implies balancing. It can be applied to many contexts and situations. Symmetry is found in geometry when a figure can be divided into two equal halves which are exact reflections of each other. In geometrical mathematics, symmetry is a very interesting concept. It is also reflecting in real life. This article will show this popular concept. Let us start with learning symmetry formula.

Symmetry

Definition

Symmetry comes from the Greek word meaning ‘to measure together’. It is widely used in the study of geometry. Thus, it means that one shape becomes exactly like another shape when we move it in some way such as turn, flip or slide. For two objects to be symmetrical, it is necessary that they must be the same size and shape.

There can also be symmetry in one object, as our face. If you draw a line of symmetry down the center of our face, we can see that the left side is a mirror image of the right side. But, not all objects have symmetry and such objects are called asymmetric.

Types

There are several types of symmetry which are as follows:

  1. Reflective or line symmetry,
  2. Rotational symmetry,
  3. Point symmetry,
  4. Translational symmetry,

Among these types, two are considered the most important and are explained in detail in the following articles-

Reflection Symmetry

What if we took a picture of ourselves, as a passport-type photograph, and drew a line straight down the middle of the face. We can notice that it seem as if one side of our face was a reflection of the other. Ideally, our passport photo is just one example of reflection symmetry. It is also known as a bilateral, line, or mirror symmetry. The line we drew to divide our face is called the line of symmetry.

Rotational Symmetry

The recycling icon in our computer is a very common symbol and the image itself is suggestive of its meaning. The arrows of the image appear to be moving in a circular manner and therefore suggesting the circular concept of recycling. So, if we rotate this image by 120 degrees, then it would look the same at all three stops. This type of symmetry is called rotational symmetry. Many shapes have rotational symmetry, like rectangles, squares, circles, and all regular polygons.

Some Important Terms

Line of Symmetry

It is a line about which the figure can be folded so that the two parts of the figure may coincide. For regular polygons, there are many lines of symmetry. The number of lines of symmetry for some common polygons is as given below.

Type of Regular Polygon Number of Lines of Symmetry
Equilateral Triangle 3
Square 4
Regular Pentagon 5
Regular Hexagon 6

Centre and Angle of Rotation

The center of rotation is a fixed point from which an object is rotated. Also, the angle of rotation is the angle by which an object rotates. This rotation can be either clockwise or anticlockwise and angle can be up to 360 degrees.

Order of Rotational Symmetry

The order of rotational symmetry is the number of times an object will look exactly the same after a complete turn. Such as the order of symmetry for a square is 4 and for an equilateral triangle, it is 3.

Solved Examples

Q: Give any three examples of shapes that have no line of symmetry.

Solution: Scalene triangle, quadrilateral, and parallelograms are examples of shapes that have no line of symmetry.

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