Line of Symmetry

The line of symmetry is an imaginary line that divides a shape or an object into identical halves. It is also called the axis of symmetry or the mirror line since it divides the figure symmetrically.

The diagram below shows how a line of symmetry divides a shape into identical halves that are mirror images.

Types

Based on the orientation of the symmetry line of an object, lines of symmetry are of 3 types:

Vertical Line of Symmetry

It is an imaginary vertical line that goes from top to bottom (or vice-versa) in an object and divides it into right and left mirror halves. For example, a club shape has a vertical line of symmetry.

Horizontal Line of Symmetry

It is an imaginary horizontal line that goes from right to left (or vice-versa) in an object and divides it into top and bottom mirror halves. For example, an arrow has a horizontal line of symmetry.

Diagonal Line of Symmetry

It is an imaginary diagonal or skew line that goes slanting in an object and divides it into mirror halves, as in the case of a square.

Number

An object can have one or more lines of symmetry. Some examples involving real-life objects are:

In geometry, the number of lines of symmetry varies according to the shape as shown in case of polygons.

In triangles, the line of symmetry can be one, three, or zero, depending upon its type.
In quadrilaterals, the line of symmetry can be one, two, four, or zero based on the shape.
In regular polygons, the line of symmetry can be multiple depending on the number of sides.
A circle has infinite lines of symmetry as an infinite number of lines pass through its center.

Solved Examples

Find the number of lines of symmetry in the shapes given along side.

The first shape is asymmetric. So it has no lines of symmetry.
The second shape has 4 lines of symmetry.
The third shape has only 1 line of symmetry.

FAQs

Q1. How many lines of symmetry does a rhombus have?

Ans. A rhombus has 2 lines of symmetry. They are the diagonals.

Q2. How many lines of symmetry does the isosceles trapezoid have?

Ans. An isosceles trapezoid has 1 line of symmetry, which is the vertical line of symmetry.

Q3. How many lines of symmetry does an equilateral triangle have?

Ans. An equilateral triangle has 3 lines of symmetry.

Q5. How many lines of symmetry does a parallelogram have?

Ans. A parallelogram has no line of symmetry.

Q6. How many lines of symmetry does a circle have?

Ans. A circle has infinite number of symmetry.

Last modified on August 3rd, 2023