Symmetry - Sub Topics

In this chapter, you will find a more detailed definition of symmetry. Symmetry is when an object is evenly balanced with one side mirroring the other as if having a twin but in the world of shapes! Symmetry is a fundamental concept in geometry that plays a crucial role in understanding the balance and order within shapes and patterns. This introduction sets the stage for exploring the fascinating world of symmetry, where we'll cover its different uses and significance in various fields.

  • Symmetry
  • Line of Symmetry
  • Types of lines of symmetry
  • Rotational Symmetry
  • Centre of Rotation
  • Order of Rotational Symmetry
  • Solved Questions on Symmetry
  • Symmetry

    Symmetry is a method to balance an object when it can be divided into two perfectly identical halves. It is like a special kind of balance and sameness in a shape. This means that when you split it up into two pieces, one side of an object looks exactly like the other.

    In order to create an imaginary line in the middle of it, we could have divided it into two parts. The figure shows a symmetric flower.


    Symmetric and asymmetric pots are shown in the figure.


    Line of Symmetry

    The line of symmetry is an imaginary line drawn through a shape to achieve symmetry. There may be a single or several lines of symmetry in the shape.

    Imagine a sheet of paper folded in half so that you can better understand symmetry. When the two sides are in perfect alignment it is possible to achieve symmetry. The "line of symmetry" is referred to as the fold itself.


    Types of lines of symmetry are as follows:

    a. Vertical Line of Symmetry

    If a vertical line divides an object into two identical halves, it is called a vertical line of symmetry.


    b. Horizontal Line of Symmetry

    If a horizontal line divides an object into two identical halves, it is called a horizontal line of symmetry.


    c. Diagonal Line of Symmetry

    If a diagonal divides an object into two identical halves, it is called a diagonal line of symmetry.


    Line of symmetry of alphabets:

    Some alphabet letters have no lines of symmetry while others may have one or more lines of symmetry. The lines of symmetry of the alphabet are shown below:


    The letters F, G, J, L, N, P, Q, R, S and Z have no line of symmetry as the letters cannot be divided into two or more equal halves.

    The letters A, B, C, D, E, K and M have exactly one line of symmetry.

    The letters H, I and X have two lines of symmetry.

    Line of symmetry of digits:

    Some digits have no lines of symmetry while others may have one or more lines of symmetry. The line of symmetry of digits is shown below:


    Digits 1, 2, 4, 5, 6, 7 and 9 do not have any lines of symmetry.

    Digit 3 has exactly one line of symmetry.

    Digits 0 and 8 have two lines of symmetry.

    The following diagram illustrates lines of symmetry for some figures:


    Example:  How many lines of symmetry does the given figure have?


    a) No line of symmetry
    b) One line of symmetry
    c) Two lines of symmetry
    d) Four lines of symmetry

    Answer: b) One line of symmetry

    Explanation: There is only one line of symmetry, shown as:


    Rotational Symmetry

    Rotational symmetry is a geometric property where an object retains its symmetrical appearance when rotated around its vertical axis.


    The given figure has rotational symmetry.


    The given figure has no rotational symmetry.


    Centre of Rotation

    The centre of rotation is a point within an object where rotational symmetry takes place. A point where the plane figure will rotate is the centre of rotation. During the rotation, this point is not moving.

    In a wheel, the centre of rotation is shown as follows:


    The centre of rotation of the hexagon is shown as:


    Order of Rotational Symmetry

    Order of symmetry describes the number of times a figure or object appears identical when rotated through a complete angle of 360°. The extent of rotation symmetry acquired by a figure is defined by this concept.

    Let’s learn about the order of rotation.

    → The order of symmetry is the number of times a figure can be moved around and still look the same as it did before it was moved. The kite looks the same only once after 360° rotation. Therefore, the order of symmetry of a kite is one. 

    The rotation of a kite clockwise is shown as


    The rotation of a kite anticlockwise is shown as


    → The hexagon looks the same after a 60° rotation. It looks the same six times to complete the rotation. Therefore, the order of symmetry is six.


    The order of rotational symmetry of common polygons is shown as:


    Example: Match the figures in Column I with their order of rotational symmetry in Column II.


    a) (A) - (2); (B) - (1); (C) - (3); (D) - (4)
    b) (A) - (2); (B) - (1); (C) - (4); (D) - (3)
    c) (A) - (2); (B) - (3); (C) - (4); (D) - (1)
    d) (A) - (2); (B) - (4); (C) - (3); (D) - (1)

    Answer: b) (A) - (2); (B) - (1); (C) - (4); (D) - (3)

    Explanation: The order of rotational symmetry is shown as:


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