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Line of Symmetry

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Last updated date: 22nd Mar 2024
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Definition of Line of Symmetry

In Mathematics, the term Symmetry can be defined as a mirror image of an object, when an image of an object appears similar to the original image even after turning or flipping the object. Then this is called symmetry. The symmetry can be found in different patterns. We all have often heard of the term symmetry in normal life.


The line of symmetry definition states that it is the line that passes through the center of the structure, object, and any shape. This line is referred to as the axis or imaginary line of the object. Now we are aware of the term symmetry of geometry that when an object has a line of symmetry then in two halves of an object where one-half is the mirror image of the other half.


The line that is considered as imaginary along which we can fold a figure or pattern to get the symmetrical halves is known as the line of symmetry. It can be also referred to as the axis of symmetry. The line symmetry is also called a mirror line as it shows two reflections of an image. Therefore, it can be termed as a type of reflection symmetry. It usually divides an object into two halves. Asymmetric objects possess no line of symmetry.


Types of Lines of Symmetry

The lines of symmetry can be any type of combination such as vertical, horizontal, and diagonal. Hence there are mainly three types of lines of symmetry based on the line of symmetry definition. They are as follows.

  • Vertical Line of Symmetry

  • Horizontal Line of Symmetry

  • Diagonal Line of Symmetry


Now know in detail about each type of symmetry.

  • Vertical Line of Symmetry

When the axis of the figure, shape, or pattern divides it into two identical equal halves vertically then, this type of symmetry is called a vertical line of symmetry. Some of the English alphabets, such as A, H, M, O, U, show the vertical lines of symmetry when they are divided vertically in symmetry.


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  • Horizontal Line of Symmetry

In the Horizontal line of symmetry, the axis of a shape divides it into two identical halves. Hence this symmetry is called the horizontal line of symmetry. Hence the axis here crosses across the shape to cut it into two equal parts. The English alphabets such as B, C, H, E are some examples that possess horizontal lines of symmetry.


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  • Diagonal Line of Symmetry

In a diagonal line of symmetry, A shape is divided into two identical halves through the diagonal. For example, when we split a square shape across the corners to form two identical halves, then we observe the diagonal line of symmetry.


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A line of symmetry is an axis along which we can cut an object to obtain identical halves. These objects may have one, two, or multiple lines of symmetry. On the basis of the number of lines of symmetry, it can be divided into the following types.


  • Three Lines of Symmetry

The best example of three lines of symmetry is an equilateral triangle. The symmetry is found along the three medians of the triangle.


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  • Four Lines of Symmetry

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


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The following patterns also have four lines of symmetry.


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  • Five Lines of Symmetry

We observe five lines of symmetry in a regular pentagon. We can see the lines of the symmetry in the following figure that they divide the pentagon into ten symmetrical halves.


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The following pattern of a star also has five lines of symmetry.


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  • Six Lines of Symmetry

A regular hexagon has six lines of symmetry. Among the six lines of symmetry, three lines of symmetry are joining the opposite vertices, and the rest are joining the mid-points of the opposite sides.


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  • Infinite Lines of Symmetry

A circle is a geometrical shape that has infinite or no lines of symmetry. It has symmetry along all its diameters.


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Line of Symmetry Examples

For an example of a line of symmetry, we can cut an apple into two equal halves; then, we would find that one piece of apple is symmetrical with another. One more common example is that if we cut a square into two equal halves, then this two haves will be symmetrical in shape. These examples are also applicable to different geometric structures, which can also be considered for line symmetry such as triangle, rectangle, circle. Some of the examples of the line of symmetry for different figures are as follows.


  • Example 1 - We observe different types of lines of symmetry in a triangle, such as one, two, or even no lines of symmetry depending on the type of triangle. An Equilateral Triangle usually has three lines of symmetry.

  • Example 2 - A Quadrilateral used to have two or four or no lines of symmetry.

  • Example 3 - A regular pentagon has five lines of symmetry


Do You Know?

  • All regular polygons are symmetrical in shape, and the number of sides is the same as the lines of symmetry.

  • The image of an object and object are symmetrical with reference to its mirror line.

  • If a figure has point symmetry; has rotational symmetry of 180º.


Symmetry can be found in two halves of an object as it is a balanced and proportionate similarity hence one-half of the object is the mirror image of the other half. The shape that is not symmetrical is known as asymmetrical. Symmetric objects can be seen all around us in nature, architecture, and art. Hence the line of symmetry is an important concept of mathematics.

Conclusion

We frequently notice symmetry in our surroundings. When the exact reflection or mirror image of a line, shape, or object is created, we say there is symmetry.


The axis or imaginary line that passes through the center of the shape or object and divides it into identical halves is known as the line of symmetry.


For example, if we fold the figure cut out exactly in the middle vertically, the halves will be congruent. The fold line is the line of symmetry.

FAQs on Line of Symmetry

1. What does symmetry mean in mathematics?

The concept of symmetry is quite useful in mathematics. Especially it has great use in geometry. The term symmetry in mathematics is defined as the shape which possesses an exact resemblance to the other parts when the shape is being divided into two or more equal parts. Hence such figures and shapes are referred to as symmetrical. There are many shapes that do not have regularity in shape and cannot be divided into equal parts. Such shapes are called asymmetrical shapes. In this case, the concept of line of symmetry is not applicable.

2. What is a line of symmetry?

A line that divides a shape, figure, or any pattern in identical halves is called the line of symmetry. The line of symmetry is also called the mirror line because it shows two reflections of an image that coincide. Therefore, it can be termed as a type of reflection symmetry. There are many types of symmetry, such as no line of symmetry, infinite lines of symmetry, one line of symmetry, and two lines of symmetry.

3. What are asymmetrical shapes?

There are some shapes, figures, and images that are not divisible into identical halves. In this type of object, we are not able to draw lines of symmetry. These shapes and images are called asymmetrical shapes images. For example- a parallelogram is an asymmetrical shape as it does not have a line of symmetry. Asymmetric objects possess no line of symmetry. Hence the existence of asymmetry exists when the two halves of any object do not match or are unequal. We can observe various examples of asymmetry in normal life.