Symmetry
Symmetry
What is Symmetry?
When a shape is divided from the center, it is divided into two identical halves. Or you can say when a figure is divided into two halves one is the mirror image of the other.
Consider the below shape of a butterfly, if it is folded from the exact center, it will be identical on both sides.
Examples of symmetrical shapes are found all around us, like a flower, a butterfly, etc.
Line of Symmetry
The figure is divided along the center line which is an imaginary line this line is called the axis of symmetry or the line of symmetry.
The line of symmetry can be
- horizontal
- vertical
- diagonal.
There can be
- one
- two
- more lines of symmetry.
Example of a figure having one line of symmetry
From the below figure the rectangle is divided horizontally and vertically. The dashed line is called the line of symmetry. There can be two lines of symmetry in a rectangle.
Example of a figure having infinite number of lines of symmetry.The best example is a circle with an infinite number of lines of symmetry.
Real-life examples of symmetry
- Reflection of trees in clear water.
- Reflection of mountains in a lake.
- Butterflies are identical on both sides.
- Some human faces are identical on the left and right sides.
Line of Symmetry for Regular Polygons
Equilateral Triangle
- All three sides of an equilateral triangle are equal.
- It has three lines of symmetry.
Square
- All four sides are equal.
- It has four lines of symmetry.
Regular Pentagon
- A regular pentagon has five equal sides.
- So it has five lines of symmetry.
Regular Hexagon
- A regular pentagon has six equal sides.
- So it has six lines of symmetry.
Regular Heptagon
- A regular heptagon has seven equal sides.
- So it has seven lines of symmetry.
Regular Octagon
- A regular octagon has eight equal sides.
- So it has eight lines of symmetry.
So we can say that a regular polygon has as many lines of symmetry as the number of sides it has.
Types of Symmetry
Symmetry in Maths is divided into two types of symmetry.
Types of symmetry are as follows:
- Reflection symmetry
- Rotational Symmetry
Reflection Symmetry:
- when a figure is divided into two identical halves such that one is a mirror image of the other then it is called reflection symmetry.
Example:
Rotational Symmetry:
- A figure that looks exactly the same after rotation as it was before rotation is called rotational symmetry.
- When an object rotates, its size and shape do not change. Rotation can be clockwise or anticlockwise.
- The fixed point about which the object is rotated is called the center of rotation.
Example :
Order of Rotational Symmetry
- The number of distinct orientations in which the shape looks the same as the original is called its order of rotational symmetry.
- A full turn means a rotation of about 360 degree. In a full turn, there are mainly 4 rotational positions
- Rotation through 90 degree, which is called a quarter turn.
- Rotation through 180 degree, which is called half turn.
- Rotation through 270 degree, which is called a three - fourth turn.
- Rotation through 360 degree , which is called a full turn.
Line of Symmetry of the English Alphabets
- Vertical line of symmetry:
- Horizontal line of symmetry:
- Both vertical and horizontal line of symmetry:
- No line of symmetry:
Fun Facts on Symmetry
- A kaleidoscope has mirrors inside it that produce images that have multiple lines of symmetry. The angle between the mirror decides the number of lines of symmetry.
- We may have observed several symmetrical objects in our daily life like rangolis or kolams. The striking aspect of symmetry can be observed in rangoli designs. These designs are famous in India for their unique and symmetrical patterns. They depict the colorful science of symmetry.
Quiz Time:
.jpg)
