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Introduction
Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”.
Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry (Fig). We can see that the two halves are mirror images of each other. If we place a mirror on the fold then the image of one side of the picture will fall exactly on the other side of the picture. When it happens, the fold, which is the mirror line, is a line of symmetry (or an axis of symmetry) for the picture.

When we fold them along the dotted line, one half of the drawing would fit exactly over the other half.
 

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Symmetry is quite a common term used in day to day life. When we see certain figures with evenly balanced proportions, we say, “They are symmetrical”.

These pictures of architectural marvel are beautiful because of their symmetry. Suppose we could fold a picture in half such that the left and right halves match exactly then the picture is said to have line symmetry.

 

Chapter 13

Symmetry

Introduction to symmetry

In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
If an object is symmetrical, it means that it is equal on both sides. Suppose, if we fold a paper such that half of the paper coincides with the other half of the paper, then the paper has symmetry. 

Symmetry can be defined for both regular and irregular shapes. For example, a square is a regular (all sides are equal) and a rectangle is an irregular shape (since only opposite sides are equal). The symmetries for both shapes are different

Two lines of symmetry

Line Symmetry

Figure is symmetrical only about one axis. It may be horizontal or vertical. The word ATOYOTA has one axis of symmetry along the axis passing through Y.

Figure is symmetrical with only about two lines. The lines may be vertical and horizontal lines as viewed in the letters H and X. Thus, we can see here two lines symmetry.

Three or more lines of symmetry

An example of three lines of symmetry is an equilateral triangle. Here, the mirror line passes from the vertex to the opposite side dividing the triangle into two equal right triangles.

Four lines of symmetry can be seen in a square, which has all the sides equal. 

Reflection symmetry

Reflection symmetry is a type of symmetry in which one-half of the object reflects the other half of the object. It is also called mirror symmetry or line of symmetry. A classic example of reflection symmetry can be observed in nature, as represented in the below figure.

 

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