Line Symmetry

When we see certain figures with evenly balanced proportions, we say, “* They are symmetrical”*.

This Topic gives an overview of;

- Line Symmetry
- Making Symmetric Figures:
- Ink-blot Devils
- Inked-string patterns

- Symmetry of Different Geometrical Figures
- kite
- Rectangle
- Equilateral Triangle
- Circle

A figure can have line symmetry if a line can be drawn dividing it into two equal halves. The line is called the * Line of symmetry*. More clearly, 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 .We can see that the two halves are mirror images of each other.

Examples of line symmetry can also be found in many of our ancient and modern buildings. 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. Here are some examples of symmetry. The line symmetry is shown in dotted line.

You can make different symmetrical figures to understand the concept of line of symmetry. Take a piece of paper. Fold it in half. Spill a few drops of ink on one half side. Now press the halves together. The resulting figure will be symmetric and you make different patterns. This is called ink blot patterns.

Fold a paper in half. On one half-portion, arrange short lengths of string dipped in a variety of coloured inks or paints. Now press the two halves. The resulting figure would be symmetric. Fold the paper in different ways to produce two identical halves. This is called inked string Patterns.

Take two such identical set-squares. Place them side by side to form a ‘kite’. A kite shape has only** one line** of symmetry.

Take a rectangular sheet (like a post-card). Fold it once lengthwise so that one half fits exactly over the other half. Open it up now and again fold on its width in the same way. A rectangle has **two lines** of symmetry.

Take a square piece of paper. Fold it into half vertically; fold it again into half horizontally. (i.e. you have folded it twice). Now open out the folds and again fold the square into half (for a third time now), but this time along a diagonal, as shown in the figure. Again open it and fold it into half (for the fourth time), but this time along the other diagonal, as shown in the figure. Open out the fold. It forms in the shape of an equilateral triangle. An equilateral triangle has **three lines **of symmetry.

Draw a circle of any radius. Fold the circle in the middle so that the center of the circle lies on the fold we find that we can fold it in many ways. Thus circle has an** infinite number of lines** of symmetry.

A shape may have just one or more than one lines of symmetry. When completing a given figure against a given line of symmetry, make sure that:

- Each part of the constructed figure is equal in measurement to its corresponding part in the given figure.
- Each point on the given figure and its corresponding point on the constructed figure are at the same distance from the line of symmetry.

- We learnt that, A figure has line symmetry if a line can be drawn dividing the figure into two identical parts. The line is called a line of symmetry.

- A figure may have no line of symmetry, only one line of symmetry, two lines of symmetry or multiple lines of symmetry. Some of the examples are:
- A scalene triangle has no line of symmetry.
- An isosceles triangle has only one line of symmetry.
- A rectangle has two lines of symmetry.
- An equilateral triangle has three lines of symmetry.
- A circle has an infinite number of lines of symmetry.

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