# Symmetrical Shapes

Symmetrical shapes are discussed here in this topic.

Any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical. The line which divides the shape is called the symmetry. So, if we place a mirror on the line of symmetry we can see the complete image.

When a symmetrical shape is folded along the line of symmetry, one half of the shape exactly lies over the other half which shows that one half of the shape is exactly the same as the other half.

In our surroundings, we find many figures and objects each of these figures or objects can be folded along a straight line in such a way that it is divided equally into two halves. The concept of symmetry has been beautifully used in the construction of monuments like the Taj Mahal, the Red Fort, the Hawa Mahal, etc.

The dotted line which divides the figure into two equal parts is called its Line of Symmetry.

There are many things around us which are symmetrical. We can see symmetry in Nature as well. Look at the following pictures and observe.

We know that in one symmetrical figure may have more than one line of symmetry.

A line of symmetry can be drawn vertically as well as horizontally depending upon the shape of the object.

Some symmetrical shapes have one line of symmetry, some have two and some have more than two, as shown below:

(i) Examples of the shapes having one-line symmetry:

One-Line Symmetry

Some shape may have two or more lines of symmetry like a circle has infinite lines of symmetry. A square has four lines of symmetry. A rectangle has two lines of symmetry.

(ii) Examples of the shapes having two - lines symmetry:

Two – Lines Symmetry

(iii) Examples of the shapes having three - lines symmetry:

Three – Lines Symmetry

(iv) Examples of the shapes having four - lines symmetry:

Four – Lines Symmetry

(v) Examples of the shapes having many - lines symmetry:

Many – Lines Symmetry

The line which divides the shape into two equal parts from top to bottom is called the vertical line of symmetry.

Some objects have a horizontal line of symmetry which divides the shape into equal parts from left to right side.

Observe the following letters of English alphabet:

We see that each of the letters B, D, E, M has only one line of symmetry whereas each the letters H, I, O and X has two lines of symmetry. We can also see that each of the letter F, G, L, etc. has no line of symmetry.

A figure that does not have any line of symmetry is called non-symmetrical.

Some figures may have more than two lines of symmetry.

Thus we may conclude that;

(i) Some shapes have no line of symmetry,

(ii) some have one line of symmetry,

(iii) some have two,

(iv) some have three and

(v) some have many lines of symmetry.

A circle has innumerable lines of symmetry that pass through its centre,

The knowledge of symmetrical shapes and lines of symmetry is very useful for making symmetrical designs.

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