Reflection Symmetry - Maths

Symmetrical objects are seen in daily life in terms of furniture, gadgets, toys etc. If an object or a figure can be split into two halves, then it contains symmetrical nature. The line of symmetry is nothing but a line that cuts objects into two parts or congruent halves. This line can also be called a mirror line. In reflection symmetry, the first half is a mirror image of the second half. Objects are allowed to have more than one symmetric line along which the objects can be divided symmetrically. Reflection symmetry is obtained if a shape has one or more lines of symmetry.

The following are some of the important aspects of reflection symmetry:

A shape or figure can have one or more symmetric lines.
The direction of the line of symmetry is not fixed and is flexible.
Both the halves are considered to be congruent and are mirror images of one another.

Reflection symmetry

For example, imagine a shape of a diamond held vertically. It is easy to divide the diamond into two equal parts along the central vertical line. This vertical line is called a mirror line or the line of symmetry. Moreover, the diamond cannot be further folded to get more equal halves. So, diamond has only one reflection symmetry.

But many such objects or figures are capable of possessing more than one line of symmetry. Example: a rectangle.

A rectangle can effortlessly be divided into two halves along the vertical line and the horizontal line. Hence, this shape has two axes of reflection symmetry.

It is necessary to understand that not all shapes or figures have reflection symmetry. There are enormous numbers of shapes that cannot be split into perfect and equal halves. They are said to be asymmetrical. An example of this would be a scalene triangle. It is impossible to split this triangle into two halves, and hence it does not possess reflection symmetry property.

The beauty of reflection symmetry is that it can easily be illustrated by everyday objects like below mentioned:

A Circle: A circle can be divided into many equal parts along its diameter, and the fact that an infinite amount of diameters can simply be drawn for a circle is considered to have infinite lines of symmetry.

Reflection symmetry

A Square: It can be simply divided into equal halves in terms of four different ways. They are horizontal separation, vertical separation and two diagonal separations. Hence a square is termed to have four lines of symmetry.

Reflection symmetry

An Equilateral Triangle: All the three sides of an equilateral triangle are equal, and it can be divided into equal halves by drawing lines from the midpoint of a side which joins the opposite vertex. Hence, an equilateral triangle can seem to have three lines of symmetry.
An Isosceles Triangle: It has two equal sides, and therefore the line of symmetry is 1.

Reflection symmetry

Apart from 2D figures, there are 3D objects which possess the same property as well. For those objects, planes are considered as lines. Some real-time examples of this include the reflection of mountains in rivers or lakes. Here the symmetry line is the ground plane.