Chapter Notes: Symmetry

Symmetry Class 6 Notes Maths Chapter 12

13. Symmetry

Line Symmetry:

A figure can have line symmetry if a line can be drawn dividing it into two equal halves. The line is called the line of symmetry.

A figure can have line symmetry if a line can be drawn dividing it into two equal halves. The line is called the line of symmetry. We can find examples of objects showing line symmetry in nature. For example, a butterfly, some leaves and flowers show line symmetry.

Examples of line symmetry can also be found in many of our ancient and modern buildings.

Objects that show line symmetry appear more balanced and beautiful.

A kite shape has only one line of symmetry.

A rectangle has two lines of symmetry.

An equilateral triangle has three lines of symmetry.

Page 55

A circle has an infinite number of lines of symmetry.

A shape may have just one or more than one lines of symmetry. When completing a given figure against a given line of symmetry, make sure that:
Each part of the constructed figure is equal in measurement to its corresponding part in the given figure.
Each point on the given figure and its corresponding point on the constructed figure are at the same distance from the line of symmetry.

Mirror Symmetry

The line of symmetry is related to mirror reflection.

Note Page 56

The line of symmetry is related to mirror reflection. An object and its mirror image are equal in shape and size. An object and its image are always at the same distance from the surface of a mirror, which is called the mirror line.

The left and the right sides of an object appear inverted in a mirror. An object and its image show mirror symmetry, with the mirror line being the line of symmetry.

Letters written from right to left, appear written from left to right in their mirror image. Letters like A, M and U appear the same in their mirror image. The letters A, H, I, M, O, T, U, V, W, X and Y appear the same in their mirror image.

All the other letters of the alphabet appear reversed in their mirror image. Symmetry has plenty of applications in real life, as in art, architecture, textiles designing, geometrical reasoning, Kolams, Rangoli, etc.

The document Symmetry Class 6 Notes Maths Chapter 12 is a part of the Class 6 Course Mathematics (Maths) Class 6.
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FAQs on Symmetry Class 6 Notes Maths Chapter 12

 1. What is symmetry?
Ans. Symmetry is a concept in mathematics and art that refers to a balanced arrangement of parts or elements. It occurs when an object or a shape can be divided into two or more identical or nearly identical parts that mirror each other.
 2. How is symmetry used in design and architecture?
Ans. Symmetry is often used in design and architecture to create a sense of balance and harmony. It can be seen in the arrangement of windows in a building, the layout of a garden, or the patterns in a wallpaper. Symmetry helps to create visually appealing and aesthetically pleasing designs.
 3. What are the different types of symmetry?
Ans. There are several types of symmetry, including: - Reflectional Symmetry: Also known as mirror or bilateral symmetry, it occurs when an object can be divided into two equal halves that are mirror images of each other. - Rotational Symmetry: It occurs when an object can be rotated around a central point and still appear the same in multiple positions. - Translational Symmetry: It occurs when an object can be shifted or translated in a certain direction and still maintain its original shape. - Glide Symmetry: It occurs when an object can be reflected and translated simultaneously. - Rotoreflectional Symmetry: It is a combination of rotational and reflectional symmetry, where an object can be rotated and reflected at the same time.
 4. How is symmetry used in nature?
Ans. Symmetry is prevalent in nature and can be observed in various organisms and natural patterns. For example, many animals exhibit bilateral symmetry, where their left and right sides are roughly mirror images of each other. Flowers often display radial symmetry, with their petals arranged symmetrically around a central axis. Snowflakes also exhibit intricate and symmetrical patterns due to the molecular structure of ice.
 5. What is the significance of symmetry in mathematics?
Ans. Symmetry plays a crucial role in mathematics as it helps in understanding patterns, shapes, and relationships. It allows mathematicians to study and analyze the properties of objects and equations by identifying and applying symmetrical transformations. Symmetry is also used in various branches of mathematics, such as geometry, algebra, and group theory, to solve problems and make connections between different mathematical concepts.

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