Line of Symmetry: Definition, Types & Examples

Line of symmetry is a line that divides a shape or figure into two halves. These two halves are the reflection of each other. A line of Symmetry is an imaginary line or axis that always passes through the center of a shape or a figure. Since one-half reflects the other half, it is also known as reflection or mirror symmetry. The line of symmetry of shapes like circles, squares, equilateral triangles, and other polygons can be drawn in vertical, horizontal, slanting, etc. directions. 

Also Read: Rotational Symmetry

Key Terms: Symmetry, Line Symmetry, Horizontal Line Symmetry, Vertical Line Symmetry, Axis, figures, shapes.

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Line of Symmetry

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Line of symmetry is an imaginary axis or line that passes through the center of a body. It divides the body or shape into two halves. These two halves reflect each other. The line of symmetry is also known as the axis of symmetry. As the two halves reflect each other, it is also termed as reflection or mirror symmetry. A figure may have: 

• No Line of Symmetry (for the asymmetrical figure)
• One Line of Symmetry 
• Two Line of Symmetry 
• Multiple (more than 2) Line of Symmetry
• Infinite Line of Symmetry,

Lines of Symmetry

For example, cut an apple into two pieces, the one piece is symmetric with another piece or a mirror image of another piece. Similarly, an equilateral triangle can be divided into halves. The two triangles formed are the right-angled triangles. Asymmetrical Figures are defined as irregular figures that cannot be divided into two equal parts. Hence, the concept of line of symmetrical is not applicable for such figures.

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Types of Line of Symmetry

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Line of Symmetry can be a combination of horizontal, vertical, and diagonal. In actuality, there are three types of axis or lines of symmetry. 

1. Horizontal Line of Symmetry
2. Vertical Line of Symmetry
3. Diagonal Line of Symmetry

Horizontal Line of Symmetry 

Any horizontal line or axis that passes through the center of a figure and divides it into two halves, that line is known as the Horizontal Line of Symmetry. In English alphabets, B, C, D, E, H, K shows horizontal symmetry. 

Horizontal Line of Symmetry

Vertical Line of Symmetry

A vertical axis that passes through the center of a figure and divides it into two halves, that line is known as the Vertical Line of Symmetry. Alphabets like A, H, I, M, O, U, V, W, T, Y are examples of the vertical lines of symmetry. 

Vertical line of symmetry

Note: Alphabets such as ‘H’, ‘I’, ‘O’, ‘X’ show both horizontal and vertical symmetry. This means, a shape or a figure may have either one or both lines of symmetry. Also, alphabets such as ‘F’, ‘G’, ‘L’, ‘P’, ‘Q’, ‘R’, ‘S’, ‘Z’ do not show any symmetry.

Line of symmetry in Alphabets

Diagonal Line of Symmetry

In a diagonal line of symmetry, the line (or axis) passes through the diagonal of a figure. In this symmetry, the figure is split across its corner and forms two halves. 

Diagonal Line of Symmetry

Two Lines of Symmetry

Shapes like rectangle, rhombus, and alphabets like ‘H’, ‘I’, ‘O’, ‘X’ are examples of two lines of symmetry. These two lines pass through the center of a shape intersecting each other.

Two Lines of Symmetry

Three Lines of Symmetry

An equilateral triangle shows three lines of symmetry. All three lines (axis) pass through its median that intersect at the center of a triangle.

Three Lines of Symmetry

Four Lines of Symmetry

A square shows four lines of symmetry. Out of 4, two lines (or axis) pass through the opposite vertices and the other two through the midpoints of opposite sides. 

Four Lines of Symmetry

Infinite Lines of Symmetry

Only a circle has infinite lines of symmetry. A circle is symmetric along all of its diameters. We can also say that a circle can either have infinite or no line (zero) symmetry.

Infinite Lines of Symmetry

No Line Symmetry

Shapes such as trapezoid, scalene triangle, parallelogram do not have any line of symmetry that is zero line of symmetry. Alphabets such as ‘F’, ‘G’, ‘L’, ‘P’, ‘Q’, ‘R’, ‘S’, ‘Z’ are examples of no line symmetry.

Also Read: Median of Triangle

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Symmetry in Coordinate Plane

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In the coordinate system, the graph may have symmetry about the x-axis, y-axis, origin, or about any given line. 

• A graph is said to be symmetric about the x-axis only when the point (x, y) is on the graph then (x, -y) must be on the graph.

Symmetry along x-axis

• A graph is said to be symmetric about the y-axis only when the point (x, y) is on the graph then (-x, y) must be on the graph.

Symmetry along y-axis

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Things to Remember

• Line of symmetry is an imaginary line that divides a shape of figure into two equal parts where one is a mirror image to the other.
• Horizontal line of symmetry is where the shape is divided into two equal parts horizontally.
• Vertical line of symmetry is where the shape is divided into two equal parts vertically.
• Depending on the number of lines of symmetry, it can be divided into two line symmetry (rectangle) , three line symmetry (equilateral triangle), four line symmetry (square) and infinite line symmetry (circle).
• Symmetry in Coordinate planes can be divided into symmetry along x-axis and symmetry along y-axis.

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