Line Of Symmetry - Multiples Lines Of Symmetry


You may be knowing well about the term symmetry which is defined as a balanced and a proportionate similarity which is found in two halves of an object, that is, one-half is the mirror image of the other half. Let us now learn about the line of symmetry.

Line of Symmetry

The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry. It basically divides an object into two halves. There may be one or more lines of symmetry. In fact, a shape may have:

  • No line of symmetry which implies that the figure is asymmetrical
  • Infinite lines of symmetry
  • One line of symmetry
  • Two lines of symmetry
  • Multiple (more than two) lines of symmetry

Check the symmetry article to learn more about no line of symmetry, infinite lines of symmetry, 1 and 2 lines of symmetry in detail. Here, let’s focus on shapes with multiple lines of symmetry.

Multiple Lines of Symmetry

The lines or axes may be any combination of vertical, horizontal and diagonal.

Three Lines of Symmetry:

An equilateral triangle has about three lines of symmetry. It is symmetrical along its three medians.

Three Lines of Symmetry

Some other patterns also have three lines of symmetry.

Three Lines of Symmetry

Four Lines of Symmetry:

A square is symmetrical along four lines of symmetry, two along the diagonals and two along with the midpoints of the opposite sides.

Four Lines of Symmetry

Some other patterns also have four lines of symmetry.

Four Lines of Symmetry

Five Lines of Symmetry:

A regular pentagon has around five lines of symmetry. The lines joining a vertex to the mid-point of the opposite side divides the figure into ten symmetrical halves.

Five Lines of Symmetry

Some other patterns also have five lines of symmetry, such as a star.

Five Lines of Symmetry

Six Lines of Symmetry:

A regular hexagon is said to have six lines of symmetry, 3 joining the opposite vertices and 3 joining the mid-points of the opposite sides.

Six Lines of Symmetry

Similarly, a regular polygon with N sides has N lines of symmetry.

Infinite Lines of Symmetry:

A circle has infinite or no lines of symmetry. It is symmetrical along all its diameters.

Infinite Lines of Symmetry

Also Check: Reflection Symmetry

Line of Symmetry – Examples

Some of the examples of line of symmetry for different figures are given below-

  1. A Triangle is said to have 3, 1 or even no lines of symmetry
  2. A Quadrilateral has 4 or 2 or no lines of symmetry
  3. Equilateral Triangle is said to have 3- lines of symmetry
  4. Regular Pentagon has 5 lines of symmetry
  5. A Regular Heptagon has 7 lines of symmetry

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Practise This Question

Find the length of EF, if AB =5cm and CA= 7cm, given that AD is the line of symmetry for the figure.