Line Symmetry

Line symmetry is a type of symmetry where one-half of the object reflects the other half of the object across the line. In simple words, we can say that when an object is divided into two equal parts with a line, then the two sides of the line look the same. It is also known as mirror symmetry or reflection symmetry. For example, the wings of butterflies are identical on both sides, the human face also shows a line symmetry.

In this article, we will discuss the concept of line of symmetry and its meaning. We will also explore the line symmetry of different shapes in geometry and how many lines of symmetry each shape has. We will also solve various examples for a better understanding of the concept.

Line symmetry is a type of symmetry about reflections. When there is at least one line in an object that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as line symmetry or reflection symmetry. The line of symmetry can be in any direction - horizontal, vertical, slanting, diagonal, etc. So, a line of symmetry can be considered as an imaginary axis/line which divided a figure into two identical halves. Let us now see how a line symmetry is represented.

Line Symmetry Representation

The very first thing to check is that the object tends to have a reflection of one-half. Imagine folding a rhombus or square along each line of symmetry and each of the half matching up perfectly, then this is symmetry. Thus, a shape has to have at least one line of symmetry to be considered as a shape with line symmetry or mirror symmetry. It is known as mirror symmetry because for the two halves which are symmetrical, one of them follows lateral inversion.

The line of symmetry also known as a mirror line is a line that divides an object into two identical pieces. Here, we have a square and we can fold it into two equal halves. When a figure is folded in half, along its line of symmetry, both the halves match each other exactly. This line of symmetry is called the axis of symmetry. Observe the different patterns of the line of symmetry an object can have with the help of a given figure.

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The line of symmetry can be categorized based on the basis of its orientation as:

• Vertical Line of Symmetry: In the above shape, it can be noticed that the shape can be split into two identical halves by a standing straight line. In such a case, the line of symmetry is vertical.
• Horizontal Line of Symmetry: In the above shape, it can be noticed that the shape can be split into two equal halves when cut horizontally. In such a case, the line of symmetry is horizontal. Hence, the horizontal line of symmetry divides a shape into identical halves, when split horizontally, i.e., cut from right to left or vice-versa.
• Diagonal Line of Symmetry: In the above shape, it can be noticed that the shape can be split across the corners to form two identical halves. In such a case, the line of symmetry is diagonal. A diagonal line of symmetry divides a shape into identical halves when split across the diagonal corners.

We have plane shapes in geometry that have line symmetry such as square, rectangle, triangle, rhombus, parallelogram, etc. Some of the common examples of the line of symmetry in two-dimensional shapes are given below:

Line Symmetry in Square

A square has 4 lines of symmetry, which are lines through the opposite vertices, and the lines through the midpoints of opposites sides make up the four lines of symmetry. So, a square has 1 vertical, 1 horizontal, and 2 diagonal lines of symmetry.

Line Symmetry in Rectangle

A rectangle has two lines of symmetry, that is lines through the midpoints of opposites sides. When a rectangle is folded across its diagonals, the shape is not symmetrical. So, a rectangle has just 1 vertical and 1 horizontal line of symmetry.

Line Symmetry in Triangle

The line symmetry in a triangle depends upon its sides. If a triangle is scalene, then it has no line symmetry. If a triangle is isosceles, then it has at least one line of symmetry, and if the triangle is equilateral, then it has three lines of symmetry.

Line Symmetry in Rhombus

A rhombus has two lines of symmetry. The two diagonals of the rhombus form its lines of symmetry.

Line Symmetry in Circle

Since an infinite number of lines can be drawn inside a circle passing through its center, therefore a circle has an infinite number of lines of symmetry.

In coordinate geometry, a parabola has a line symmetry and its line of symmetry passes through its vertex. For a parabola with quadratic equation y = ax² + bx + c, the line symmetry equation is of the form x = n, where n is a real number. The line of symmetry equation is given by, x = -b/2a. Let us solve an example to understand it better.

Example: Find the line of symmetry of parabola y = x² + x - 5

Solution: Identify a, b, c in the given equation.

a = 1, b = 1, c = -5

The line symmetry is given by, x = -b/2a = -1/(2×1) = -1/2

So, the given parabola has a line of symmetry x = -1/2.

☛ Important Notes on Line Symmetry

• All regular polygons are symmetrical in shape.
• An object and its image are symmetrical with respect to its mirror line.
• Line symmetry can also be observed on inkblot paper.
• A figure can have one or more lines of line symmetry depending on its shape and structure.
• For a parabola with quadratic equation y = ax² + bx + c, line of symmetry is x = -b/2a.

☛ Related Articles

• Axis of Symmetry
• Lines of Symmetry in a Parallelogram
• Rhombus Lines of Symmetry
• How many lines of symmetry does an isosceles triangle have
• Lines of Symmetry in a Regular Octagon

What is Line Symmetry in Geometry?

When a shape or pattern is reflected in a line of symmetry or forms a mirror image, then it is considered to show a line symmetry.

What does Line Symmetry Look Like?

For any shape, line symmetry looks when a mirror line can be drawn on it, proving that both sides of the shape are exactly the same as one another.

Does a Square have Line Symmetry?

Yes, a square has a line symmetry having four lines of reflection, two on midpoints on the sides and two through the opposite vertices.

Do Lines of Symmetry have to be Straight?

In most cases, the lines of symmetry are straight only. Although lines can be horizontal, vertical, or slanting.

How Many Lines of Line Symmetry does a Rectangle Have?

A rectangle is a regular polygon having two lines of symmetry.

Does a Right Triangle have Line Symmetry?

A right-angled triangle doesn't show line symmetry. It has no line of symmetry. It just has rotational symmetry of order 1. If the right triangle is isosceles, then it has one line of symmetry.

How to Find Line of Symmetry?

We can find the line of symmetry by folding a figure into two equal halves. When the figure is folded and its two parts are identical (or reflection of each other), then we can say that it has a line symmetry.

How to Find Line of Symmetry of a Parabola?

For a parabola with quadratic equation y = ax² + bx + c, line of symmetry is x = -b/2a.

Why Does Parallelogram have No Line of Symmetry?

A parallelogram has no line of symmetry as it is impossible to fold a parallelogram into two equal halves such that each part is a mirror image of another.