Line of Symmetry: Definition, Facts and Examples

A line of symmetry is a line that splits a shape in half perfectly. This indicates that the two halves will be perfectly aligned if you fold the form along the line. Similarly, the figure would not alter if a mirror was placed along the line. You must have observed that most of the objects in our surroundings appear with a certain beauty. The organized pattern of these objects makes them look beautiful. And this kind of organized pattern is called symmetry.

Wondering what symmetry is? Let us have a look at the definition of symmetry then! An identical figure on both sides of a line is symmetrical about that line. This article will cover every detailed information about symmetry and lines of symmetry in this article.

What is Symmetry?

Consider the situation given below.

Dhruv took a sheet of paper and folded it horizontally into two halves. He pressed the crease and unfolded the paper. He darkened the creased line using a sketch pen. He performed the same activity by taking another sheet of paper and folding it vertically into two halves.

What can you say about the two halves Dhruv got in both cases?

Well, when a figure is folded into two halves such that both the halves are identical, then we say that the figure is symmetrical. Thus, the two halves that Dhruv got after unfolding the sheet of paper are identical. This phenomenon is called symmetry.

Line of Symmetry Definition

The line that divides a figure into two identical halves is called the line of symmetry.

In the above-given figures, the red coloured line divides each figure into two halves, and suppose we fold them along that line, and we will see that one half of each figure exactly coincides with the other half. 

A figure may have zero, one, two, three or infinite lines of symmetry.

Types of Lines of Symmetry

Horizontal and Vertical Lines of Symmetry

Symmetry can be found anywhere in nature. For instance, insects, flowers, animals, designs, architectures, notebooks, shapes and alphabets, etc., have symmetry.
A shape can have a horizontal or vertical line of symmetry or both.
Have a look at a few English alphabets given below.

In the first two alphabets, \(B\) and \(C,\) the line of symmetry is horizontal, and in the following two alphabets, \(T\) and \(H,\) the line of symmetry is vertical. Thus, the horizontal line of symmetry divides the figure into the top and bottom that are mirror images of each other. In contrast, the vertical line of symmetry divides the figure into left and right, which are mirror images of each other.

Now, have a look at the alphabet \(O.\)

The alphabet \(O\) has both horizontal and vertical lines of symmetry.

Number of Lines of Symmetry

A figure can have \(0,1,2,3,….\) or an infinite number of lines of symmetry. Let us learn about each case in detail.

Zero Lines of Symmetry

Some shapes, such as scalene triangle, alphabets like \(J, K, L,\) have no or zero lines of symmetry because there is no way to fold these shapes and alphabets about a line so that the two halves fit precisely on top of one another.

One Line of Symmetry

Some figures are symmetrical, only about one axis. It may be horizontal or vertical. 

Observe the below-given figures:

These figures have only one line of symmetry as they can be folded in only one way to get identical halves.

Two Lines of Symmetry

Some figures are symmetrical with only about two lines. The lines may be vertical and horizontal, as viewed in the letters \(H\) and \(X.\) Another example with only two lines of symmetry is a rectangle.

Three Lines of Symmetry

Have a quick look at the figures given below.

All the above-given figures and patterns have \(3\) lines of symmetry.

Four Lines of Symmetry

Now, look at the figures given below,

All the above-given figures and patterns have \(4\) lines of symmetry.

Five Lines of Symmetry

Look at the figures given below. All the given figures have \(5\) lines of symmetry.

Six Lines of Symmetry

Have a look at the figures and patterns given below. All the given figures possess \(6\) lines of symmetry.

Infinite Lines of Symmetry

Some figures have not one or two but infinite lines passing through them, and the figure is still symmetrical. Example: a circle. The infinite number of lines passes through the point symmetry about the centre \(O\) with all possible diameters.

Lines of Symmetry for Regular Polygons

A polygon is a closed shape made by \(3\) or more line segments. Therefore, all sides have the same length in a regular polygon, and all angles have equal measures. Each regular polygon, like an equilateral triangle, square, rhombus, regular pentagon, regular hexagon, etc., is symmetrical.

The number of lines of symmetry in a regular polygon is equal to the number of sides a regular polygon has. Let us discuss the line of symmetry of some of the regular polygons one by one in detail.

Line of Symmetry in an Equilateral Triangle: All three sides of an equilateral triangle are equal. The measure of each angle of an equilateral triangle is \({60^ \circ }.\)	An equilateral triangle has \(3\) lines of symmetry.
Line of Symmetry in a Square: All sides of a square have equal length. Each angle of a square has the same measure.	A square is a regular polygon of \(4\) sides. The types of line of symmetry in a square are \(4.\)
Line of Symmetry in a Regular Pentagon: A regular pentagon has \(5\) equal sides, and each of its angles measures \({108^ \circ }.\)	A regular pentagon has \(5\) lines of symmetry.
Line of Symmetry in a Regular Hexagon: A regular hexagon is defined as a hexagon that is both equilateral and equiangular. \(ABCDEF\) is a regular hexagon	A regular hexagon has \(6\) lines of symmetry.

Line Symmetry Formula

The axis of symmetry is a line that divides a shape into two halves, creating a mirror image of either side of the halves. Symmetry is applicable in geometry as well. Have a look at the image given below.

To find a line of symmetry, we can make use of the formula;
\(x = \frac{{ – b}}{{2a}},\) for the quadratic equation \(y = a{x^2} + bx + c,\) where \(c\) is a constant and \(a\) and \(b\) are the coefficients of \({x^2}\) and \(x.\)

Solved Examples

Q.1. Draw the lines of symmetry for the given figure and find the number of lines of symmetry.

Ans: For the given figure, we can draw a horizontal and vertical line of symmetry.

Thus, the given figure will have \(2\) lines of symmetry.

Q.2. Complete the other half of the given figure such that the dotted line is a line of symmetry.

Ans: The line which divides the figure into two identical halves is called the line of symmetry. Thus, after drawing the other half, the complete figure will be like below:

Q.3. List the numbers from \(0\) to \(9\) that do not have even a single line of symmetry.
Ans: The numbers from \(0\) to \(9\) are \(0,1,2,3,4,5,6,7,8\) and \(9.\) Out of these numbers, \(1,2,4,5,6,7\) and \(9\) have no or zero lines of symmetry.

Q.4. How many lines of symmetry does a circle have?
Ans: A circle has infinite lines of symmetry. The infinite number of lines passes through the point symmetry about the centre \(O\) with all possible diameters.

Q.5. Match the following given shapes with their number of lines of symmetry.   

Ans: Based on the shapes, we can draw the lines of symmetry. The correct match will be as follows:

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Summary

In this article, we learned the concept of symmetry and looked at many shapes and objects symmetrical in nature. We also learned about the lines of symmetry. In addition to that, we learned that particular objects, numbers, and alphabets possess vertical lines of symmetry and horizontal lines of symmetry. We also understood that many things, numbers, and alphabets have one, two, three or multiple lines of symmetry.

Frequently Asked Questions (FAQs)

Q.1. How do you find lines of symmetry?
Ans: When you divide a figure into two halves, we say a figure has line/lines of symmetry. We can find the line/lines of symmetry by dividing the shape vertically, horizontally or both.

Q.2. Explain the line of symmetry?
Ans: A line of symmetry is a line that cuts a shape exactly in half. This would mean both halves of the object or shape match exactly if you were to fold the shape along the line of symmetry. If you were to place a mirror along the line, the shape would remain unchanged. 

Q.3. Which shape has only one line of symmetry?
Ans: A kite, alphabets like \(T,U,V,W,\) numbers like \(3,8\) etc., have only one line of symmetry.

Q.4. Which figure has line symmetry?
Ans: Many shapes have line symmetry. For example, an equilateral triangle, a square, alphabets like \(A,B,E,\) numbers like \(0,3,8\) etc., have line/lines of symmetry.

Q.5. Which shape has zero lines of symmetry?
Ans: Shapes like of scalene triangle, a parallelogram, alphabets like \(F,Z,Q,R\) and numbers like \(1,2,4,5\) etc., have no or zero lines of symmetry.

Q.6. Which shape has two lines of symmetry?
Ans: Alphabets like \(H,I,O,X,\) shapes like rhombus and rectangle have two lines of symmetry.

We hope this detailed article on the line of symmetry has helped you. If you have any doubts or queries, please leave a comment down below. We will be more than happy to help you.