Table of contents  
Symmetry  
Line Symmetry  
Line Symmetry of Regular Polygon  
Rotational Symmetry 
A figure has line symmetry if a line can be drawn dividing the figure into two identical parts.The line is called the line of symmetry or axis of symmetry.
Line Symmetry Line symmetry is also known as 'reflection symmetry' because a mirror line resembles the line of symmetry, where one half is the mirror image of the other half.
Mirror Symmetry
Remember, while looking at a mirror, an object placed on the right appears to be on the left, and vice versa.
A scalene triangle, in which all the sides are of different lengths, doesn't have any line of symmetry.
Example: Copy the figures with punched holes and find the axis of symmetry for the following:
Ans: The axis of symmetry is shown by the following line.
Example: Give three examples of shapes with no line of symmetry.
Ans:
A polygon is said to be a regular polygon if: all its sides are equal in length and all its angles are equal in measure. Only regular polygons have lines of symmetry.
Regular Polygons
An equilateral triangle is regular because each of its sides has the same length, and each of its angles measures sixty degrees.
The number of lines of symmetry in a regular polygon is equal to the number of sides that it has.
A rectangle has two lines of symmetry, and an isosceles triangle has one line of symmetry.
A pentagon has five lines of symmetry.
Similarly, a regular octagon has eight sides, and therefore, it will have eight lines of symmetry, while a regular decagon has ten sides, so it will have ten
lines of symmetry.
Example: What letters of the English alphabet have reflectional symmetry (i.e. symmetry related to mirror reflection) about
(а) a vertical mirror
(b) a horizontal mirror
(c) both horizontal and vertical mirrors.
Ans:
(a) Alphabet of vertical mirror reflection symmetry are A, H, I, M, O, T, U, V, W, X, Y
(b) Alphabet of horizontal mirror reflection symmetry are B, C, D, E, H, I, K, O, X
(c) Alphabet of both horizontal and vertical mirror reflection symmetry are H, I, O, X.
If a polygon is not a regular polygon, then it is said to be an irregular polygon. Most irregular polygons do not have line symmetry. However, some of them do.
Irregular polygons
Some letters also have line symmetry.
Any object or shape is said to have rotational symmetry if it looks exactly the same at least once during a complete rotation through 360^{o} .
Rotation may be clockwise or anticlockwise.
When identifying rotational symmetry, consider:
(i) Center of rotation: During the rotation, the object rotates around a fixed point. Its shape and size do not change. This fixed point is called the centre of rotation.
(ii) Angle of rotation: It is the angle at which a shape or an object looks exactly the same during rotation.
(iii) Direction of rotation: The direction of rotation is also referred to as the sense of rotation and indicates the direction (clockwise or anticlockwise) in which bodies rotate around an axis.
(iv) Order of rotational symmetry: It can be defined as the number of times that a shape appears exactly the same during a full 360^{o} rotation.
Rotation of a square
The circle is the most symmetrical figure. It has an infinite number of lines of symmetry, as any line passing through its center serves as a line of symmetry. Additionally, the circle has rotational symmetry around its center for every possible angle. The centre of rotation of a circle is the centre of the circle.
Rotation of a circle
The Ashok Chakra in the Indian national flag has both, line symmetry and rotational symmetry.
Ashok Chakra
Letter  Line Symmetry  Rotational Symmetry 
Z  No  Yes 
H  Yes  Yes 
0  Yes  Yes 
E  Yes  No 
N  No  Yes 
C  Yes  No 
A  Yes  No 
B  Yes  No 
Example: Which of the following figures have rotational symmetry of order more than 1:
Ans:
(a) The given figure can be rotated four times at 90^{o} angles each to produce the symmetrical figures. The above figure has a rotational symmetry of order 4
(b) The given figure can be rotated three times at 120^{o} angles each to produce the symmetrical figures. The above figure has a rotational symmetry of order 3
(c) The given figure can be rotated once at 180^{o} angles each to produce the symmetrical figures. The above figure has a rotational symmetry of order 1
(d) The given figure can be rotated two times at 180^{o} angles each to produce the symmetrical figures. The above figure has a rotational symmetry of order 2
(e) The given figure can be rotated three times at 120^{o} angles each to produce the symmetrical figures. The above figure has a rotational symmetry of order 3
(f) The given figure can be rotated four times at 90^{o} angles each to produce the symmetrical figures. The above figure has a rotational symmetry of order 4
76 videos345 docs39 tests

1. What is line symmetry? 
2. What is the concept of line symmetry in regular polygons? 
3. What is rotational symmetry? 
4. How is rotational symmetry related to regular polygons? 
5. What are some examples of figures that have line symmetry and rotational symmetry? 

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