Cbse Class 6 Maths Notes Chapter 9 Symmetry

Symmetry is an interesting concept that plays a crucial role in mathematics, art, nature, and even in our daily lives. In simple terms, symmetry refers to the balanced and proportional arrangement of parts on either side of a central point or axis. It helps us understand how shapes and objects can be mirrored, rotated, or reflected in different ways. In this blog, we’ll explore the different types of symmetry, including Line of Symmetry, Reflection, Rotational Symmetry, and the Symmetries of a Circle.

1.0What is Symmetry?

Symmetry can be described as the characteristic of an object or shape that allows it to be divided into two or more identical parts. These parts can either be mirrored or rotated around a fixed point or axis. Symmetry can be observed in various natural and man-made objects, from the wings of butterflies to the architectural designs of buildings.

2.0Line of Symmetry

The Line of Symmetry is an imaginary line that splits a shape into two identical halves. If you fold a shape along this line, the two halves will overlap perfectly. This line can be vertical, horizontal, or diagonal, depending on the shape.

• For example, a square has four lines of symmetry (two diagonals and two perpendicular bisectors), whereas a circle has infinite lines of symmetry because it can be folded along any line passing through its center.

Example:

3.0Reflection Symmetry

Reflection symmetry, also known as mirror symmetry, occurs when one half of an object is a mirror image of the other half. This is possible when there is a line of symmetry dividing the object into two identical parts.

• Real-life example: The human face exhibits reflection symmetry when divided down the middle.

• A butterfly’s wings also show reflection symmetry, where each wing is a mirror image of the other.

Reflection symmetry is common in many natural forms and shapes, where the two halves mirror each other across a central line.

4.0Rotational Symmetry

A shape has rotational symmetry if it can be rotated (less than a full circle) around a central point and still look exactly the same. The number of times a shape can fit into its original position during a complete rotation is called its order of rotational symmetry.

• For example, a regular hexagon has 6 lines of rotational symmetry, because it can be rotated by 60°, 120°, 180°, 240°, 300°, and 360°, and it will still look the same at each of these positions.
• A regular square has 4 lines of rotational symmetry, as it matches its original shape at 90°, 180°, 270°, and 360° rotations.

5.0Symmetries of a Circle

• A circle is a special shape that exhibits infinite lines of symmetry. This means that you can draw a line through the center of the circle in any direction, and the two halves will always be identical. The symmetry of a circle is a perfect example of how the concept of symmetry extends to continuous shapes.
• A circle also exhibits rotational symmetry of infinite order because it can be rotated by any angle, and it will always appear the same. Whether you rotate a circle by 1°, 90°, or 180°, the circle remains unchanged.
• This infinite symmetry makes the circle a unique and fundamental shape in geometry and real-world design.

6.0Applications of Symmetry

Symmetry isn’t just an abstract concept; it has real-world applications in various fields:

• Art and Architecture: Symmetry plays a vital role in designing visually pleasing structures, from classical buildings to modern skyscrapers. The Parthenon in Greece is a perfect example of symmetry in architecture.
• Nature: The symmetry found in flowers, leaves, animal bodies, and even galaxies showcases the beauty of natural designs.
• Engineering: Symmetry helps in designing efficient mechanical parts and structures, such as gears and wheels, ensuring balance and strength.