# Chapter 14 – Symmetry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You may have heard of the term symmetry several times. But do you know that it can be explained mathematically as well? No! It has nothing to do with the symbols of addition, subtraction, multiplication or division. Stand before a mirror. What do you see? Well, you will find an identical image of yourself reflected on the other sides. The two are proportionate, and that is symmetry. You may also try to draw an imaginary line through your body longitudinally. The two halves can be described as mirror images of each other that are totally similar in all aspects. It gives you a sense of uniformity too. Well, that is referred to as symmetrical objects.

#### Mathematical Implication of Symmetry

Think about different shapes used in mathematics. When you see a shape being duplicated fully after it is moved or turned or flipped to the opposite side, it is a symmetrical representation. Take some time to draw a heart on paper. Now fold it lengthwise or cut it in half longitudinally only to find two halves of the same image on either side. Now that is symmetry! It is found in all uniform patterns present in nature. You can go ahead and create many symmetrical objects in your Arts & Crafts class too. A shape that cannot be divided into two identical halves is known to be asymmetrical.

#### Lines of Symmetry

You may want to draw a line right through the middle of a figure you have created to fold it into two exact halves. However, you cannot make use of a pencil and draw the line physically every time. Instead, you have to imagine the line to divide a particular shape symmetrically. This line that divides an object into two halves is known as a line of symmetry. While you can draw it vertically, you can also draw a horizontal or diagonal line to meet your objective. Remember that you are free to have multiple lines of symmetry for a single figure as well. Here are a few examples to help you understand the concept better:

• 1 Line – You can divide a figure symmetrically around a single axis. Look at the word “ATOYOTA.” You can draw a line through ‘Y’ to obtain two identical halves.
• 2 Lines – A figure can be made symmetrical by passing a couple of lines through it. You can do it using a vertical and a horizontal line passing through the letters H and X.
• Infinite Lines– You may pass as many lines as you want through certain figures to get symmetrical parts. The most obvious example here is a circle. Since no specific lines are forming the figure, you can divide it into multiple symmetrical parts by passing infinite lines through it.

#### Lines of Symmetry of Regular Polygons

If you think about other geometrical figures apart from a circle, then you will find it interesting to note that the closed figures known as polygons can be divided symmetrically as well. Think of a triangle; it has three sides. You can divide an equilateral triangle into symmetrical halves with the help of a line. A square can be divided similarly by two diagonal lines. You are welcome to use multiple lines of symmetry to divide other polygons such as pentagon, hexagon, heptagon, octagon and so on.

#### Symmetry Types

You can get a symmetrical figure when you rotate a figure, move it to another position or flip it completely. Symmetry is of four different types described based on varied situations:

• Translation– When an object slides about an axis, the movement is known as translation. The object moves down in the same orientation and remains the same in shape and size.
• Rotational– When you turn an object around a point, it becomes identical to itself even in position. The rotational symmetry line is therefore, a point. The angle of rotational symmetry is quite small for a figure to coincide with itself. Almost all polygons can have rotational symmetry with other objects such as petals displaying properties of symmetry and rotational symmetry too.
• Reflection– Reflexive symmetry is described as a situation where a half of the object reflects the other completely. It can also be described as a mirror image. The two longitudinal halves of a human body or a butterfly can serve as classic examples of reflection symmetry.
• Glide- A combination of reflection and translation symmetry can be described as glide symmetry. It has commutative properties that reinforce the theory that even if the objects’ order is altered, the results remain the same. You will learn more of this in higher classes once you get introduced to calculus and theories of probability.

#### Symmetry in Shapes

You will have much fun trying to identify symmetry in different shapes. Take a figure depicting half a fish horizontally, for instance. You can make use of reflexive symmetry to complete the figure by obtaining a full fish. Use rotational symmetry to draw a flower of uniform proportions. You also have to remember that not all figures happen to be symmetrical. You will come across a scalene triangle in geometry and other irregular objects in nature that do not conform to the theory of symmetry.

#### Conclusion

The idea of symmetry may be pretty obvious, but you need to examine the world around you to understand the implications and mathematical reasoning behind it. You will find it easier to organize things once you master the concept and realize how symmetry enables us to create a harmonious effect.

#### FAQs

1. What are the 4 types of symmetry?
The four types of symmetry are Translation, Rotational, Reflexive and Glide.
2. What is symmetric in math?
A figure, shape or object that can be divided into identical parts is known as a symmetric in mathematics.
3. What is symmetry and its types?
A shape that becomes exactly like the first one after it is moved, flipped or rotated is known as symmetry. It can be defined to be a mirror image of the original shape. Symmetry can be divided into 4 distinct types, namely translation, rotational, reflexive and glide.
4. What is symmetry pattern?
A pattern that produces uniformity and regularity with the shapes having different orientations is known to be a symmetrical pattern.
5. Why is symmetry important in math?
Learning symmetry in math helps students understand uniformity in nature and the abstract concepts of advanced mathematics later on in life. Connecting mathematics to other branches of study becomes simpler for the students too.

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### High School Physics

• Alternating Current
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• Acids, Bases and Salts
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### High School Math

• Algebra – Arithmatic Progressions
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### Middle School Science

• Acids, Bases And Salts
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### Middle School Math

• Addition
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• Similarity
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• Subtraction
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