Mirror Symmetry




This topic gives an overview of;


  • Reflectional Symmetry
  • Alphabet Reflection symmetry
  • Applications of Reflectional Symmetry


Reflectional Symmetry


A Reflectional Symmetry is a type of symmetry in which one half of the object is the mirror image of the other. A figure may have both horizontal and vertical lines of reflection.

An object and its image are always at the same distance from the surface of a mirror, which is called the mirror line. Line symmetry and mirror reflection are naturally related and linked to each other. If the paper is folded, the mirror line becomes the line of symmetry. The object and its image are symmetrical with reference to the mirror line.

We then say that the image is the reflection of the object in the mirror line. When an object is reflected, there is no change in the lengths and angles; i.e. the lengths and angles of the object and the corresponding lengths and angles of the image are the same. However, in one aspect there is a change, i.e. there is a difference between the object and the image. The left and the right sides of an object appear inverted in a mirror.Here is an example that shows the refelection symmetry. 



Alphabet Reflection symmetry


Letters written from right to left, appear written from left to right in their mirror image. Letters like A, M and U appear the same in their mirror image.
The letters A, H, I, M, O, T, U, V, W, X and Y appear the same in their mirror image.

All the other letters of the alphabet appear reversed in their mirror image. Here are some examples given.



Applications of Reflectional Symmetry


Symmetry has plenty of applications in real life, as in art, architecture, textiles designing, geometrical reasoning, Kolams, Rangoli, etc.


Paper decoration


Use thin rectangular coloured paper. Fold it several times and create some intricate patterns by cutting the paper in different patterns. There are plenty of lines of symmetry such decorative paper cut-outs are used for festive occasions.





A kaleidoscope uses mirrors to produce images that have several lines of symmetry. Usually, two mirrors strips forming a V shape are used. The angle between the mirrors determines the number of lines of symmetry. Make a kaleidoscope and try to learn more about the symmetric images produced.


Rangoli patterns


Kolams and Rangoli are popular in our country. Note the use of symmetry in them. Collect as many patterns as possible of these and prepare an album. Some will have line symmetry - that is, folding or mirror symmetry. All of them have rotation (turning) symmetry. So you can spin them around and on the way around they match up with own starting position at least twice.





  • The line symmetry is closely related to mirror reflection.
  • When dealing with mirror reflection, we have to take into account the left right changes in orientation.
  • Alphabets written from right to left, appear written from left to right in their mirror image.
  • Symmetry has plenty of applications in everyday life as in art, architecture, textile technology, design creations, geometrical reasoning, Kolams, Rangoli etc.


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