Chapter 13 – Symmetry

It is the imaginary line that makes the object divided into two halves. In other words, the line of symmetry makes the object symmetrical. We can have many lines of symmetry based on the object and geometrical shape. Let’s check the types of lines of symmetry.

• Single line of symmetry: In this, the object has exactly one line of symmetry passing through it. For example, a kite shape has only one line of symmetry.
• Two-line of symmetry: The objects having two lines of symmetry can be intersected at two places. The rectangle is an example of figures with two lines of symmetry.
• Multiple lines of symmetry: Any geometrical shape that can be cut into many planes to get symmetrical halves is having multiple lines of symmetry. The circle is an example of figures with multiple lines of symmetry.

If we talk about symmetry, we can classify it into four types based on the visualisation angle. You can check that object by sliding, rotating, and producing a translation motion. Let’s check these four types of symmetry along with their definition.

1. Translation Symmetry: It is an important type of symmetry and can be visualised by moving any given geometrical shape in one single line. Hence we translate that object in a line of sight or the axis. When the object is identical to its previous position in that line, we can call it a translational symmetrical object. You can visualise this by considering a hexagon sitting at any point of space A. Now we move it in the x-axis direction linearly; we will find no change in its shape and size, and find both congruent. It is an example of translational symmetry.
2. Rotational Symmetry: It is a simple concept where we rotate any given object to bring back the object in an identical position. For example, if we take a square and rotate it by 90 degrees, we get identical shapes like the initial one. If we again keep on rotating it, you will find that there is rotational symmetry at 90 degrees, 180, 270, and 360 degrees, respectively. Hence squares have four rotational symmetry.
3. Reflexive Symmetry: In this, one half of the geometrical shape is a reflection of the other half. For example, suppose we place a mirror on the line of symmetry on a square shape in between. In that case, we can find the reflection identical to the other half in that symmetry. Hence squares have reflexive symmetry.
4. Glide Symmetry: Glide symmetry is a combination of two different types of symmetry: translation and reflection symmetry. For example, we can have a circle as an example of glide symmetry. In this reflection and symmetry goes hand-in-hand with each other.

Symmetry is a beautiful topic in maths, and nature also validates it. For example, take a symmetrical leaf equal on both sides, flowers having rotational symmetry, the human body having a vertical line of symmetry, and many more instances. It’s a fundamental concept of nature that validates energy proportionality and conservation. In maths, we can start symmetry from graphs, and then slide down to symmetrical objects’ physical applications. Even alphabets have symmetry. You can try making symmetrical figures at home to understand the concept better.

• What is the definition of symmetry?

Symmetry is having equal and similar shape when cut down in any plane. For example, when we cut a circle with the axis passing through its centre, we get two congruent halves. It is called a symmetrical shape.

• What is symmetric math?

In maths, symmetry is concerned with geometrical shapes and objects. We can depict any symmetrical object on the graph or a simple paper sheet.

• What is the symmetry line?

Symmetry line is the imaginary line that can get intersected and result in two halves of that shape. We can have many symmetrical lines based on the object type. For example, a kite has only one line of symmetry, whereas a circle has infinite lines of symmetry.

• What are the two lines of symmetry?

Any object having symmetry, when passed through two different lines, is known to have two lines of symmetry. If we take the example of a rectangle, we can get two lines of symmetry. One line of symmetry passes through the length, and the other passes through the width side.

• What is symmetry in simple words?

Symmetry in simple words can be called an object having congruence and similarity when halved. Any symmetrical object can be cut into two halves.

• What are the 4 types of symmetry?

The four types of symmetry are translation, reflection, glide reflection, and rotational symmetry. All these four types are discussed above.