Perfection means creating things in flawless harmony. Have you ever wondered how architects make such perfect edifices with flawless constructions? They bring every part of their plan in the lines of symmetry thus giving their map a touch of perfection. In this chapter, we will let you know how symmetrical shapes affects the very basis of geometry.

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## Symmetrical Shapes

Symmetry forms the very basis of any geometrical figure. Today, every activity, from paintings to engineering and designing clothes and jewellery uses the idea of giving perfect symmetry in its every artefact. Symmetry brings a harmony in the design of any object, building or painting. The effect of perfect symmetry can also be seen in natural things.

In fact, natural things are the best examples of symmetrical objects. From beehives to leaves and flowers every little thing is a wondrous work of symmetry by nature. We know that a figure is in perfect symmetry if a line of symmetry passing through the center divides the figure into identical halves. The two parts coinciding at this line of symmetry is folded across this line which makes it symmetrical.

If we fold the figure given above exactly at the center, whether vertically or horizontally, both its halves shall be identical to one another. This shows that the figure is symmetrical and its line of the fold is the line of symmetry for the figure. Look at the following figure which shows different lines of symmetry:

The line of symmetry may pass through the center vertically, horizontally and diagonally. The basic idea behind any line of symmetry is to divide a figure into exactly identical halves. Here the orientation of that line does not make any difference on the geometry of that figure.

## Lines of Symmetry

The symmetrical figure is a work of symmetry despite its division into any number of parts. Dividing a figure into identical halves is the primary test of being in symmetry. There are figures and shapes that can have more than one lines of symmetry. A circle has infinite lines of symmetry. Likewise, a triangle has three lines of symmetry, while rectangle and square have four such lines which divide them into identical parts.

## Lines of Symmetry in Polygons

Polygons are closed figures that are made of three or more than three line segments. Triangle is polygon drawn with least number of line segments. Some other examples of polygons are Square, Rectangle, Pentagon, Hexagon, Septagon etc. Polygons may be regular and irregular.

For example, an equilateral triangle or a square are regular polygons while scalene triangle and a parallelogram are irregular polygons. So regular polygons are those closed figures which have all sides and angles of equal measure. An equilateral triangle has all three sides and angles equal. This makes it a symmetrical polygon.

Regular polygons are symmetrical and divided by more than one lines of symmetry to form identical parts. A rectangle is divided into symmetrical parts with the help of two lines. An equilateral triangle is divided into identical parts with the help of three lines of symmetry passing through its center**.** Likewise, four lines divide a square into perfectly symmetrical parts.

### Some More Examples on Symmetrical Shapes

- Now, let’s consider the case of a pentagon. For a pentagon to be regular and symmetrical each of its angles has to be 108°. A Pentagon is a five-sided polygon. It can be divided by five lines to make symmetrically identical parts. Only if the angles and all sides are equal, symmetrical shapes – a pentagon is possible.

- A regular hexagon is symmetrical when its equal sides are placed at an angle of 120° to each other. A hexagon is a six-sided polygon which needs a maximum of six lines to divide the figure into identical parts.

Now, as the number of sides in polygon increases, the maximum number of its line of symmetry also increases. The only condition as mentioned earlier for a polygon to be perfectly symmetrical is that it should have sides and angles making it equal.

From the above discussion, we come to a conclusion that for an object or figure to be in symmetry it is essential that the object or figure is a perfect balance of size, shape, and angles. Any irregularity in shape or angle makes that figure asymmetrical.

## Solved Examples for You

- 3,2,3,2 respectively
- 2,3,3,2 respectively
- 6,4,6,4 respectively
- None of the above

Solution: A) The figure a) has three lines of symmetry with each line dividing the figure into identical parts. In figure (b) we can see two lines dividing the whole figure into symmetrical parts. The figure in (c) has three lines of symmetry. Figure (d) is divided into identical parts with the help of only two lines. All these figures, therefore, are good examples of multiple lines of symmetry.

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