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Line of symmetry is an axis that passes through the centre of any plane figure which divides it into two equal parts or into identical halves known as the line of symmetry. This line can be called an imaginary line or an axis of the object. Symmetry is a term or a balanced and proportional similarity founded in the two halves of any object. In other words, we can say one half of the image is the mirror image of the other.
Key Terms: Symmetry, Line of Symmetry, Two line of Symmetry, Types of Symmetry
Lines of Symmetry
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Line of symmetry of an image can be defined as the balanced and the proportional similarity between the two equal halves of any image. This can cut one half of the mirror image with another half of the image.
Line of Symmetry
To understand it more clearly, suppose you fold a piece of paper from the central part so that each half side of the image will get an equal side. After opening this paper, a line will be drawn from the central part of the paper that cuts it into two halves. Hence this line of the axis of the paper is known as the Line of Symmetry.
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Types of Symmetry
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The figure that cannot be divided into two equal halves of the figure is called an asymmetrical figure. This figure does not contain any proper side to make the halves equal and perfectly balanced. For example, if you try to fold an unevenly torn paper, it will not develop any other line of symmetry.
Types of Symmetry
There are some other figures that can divide the line of symmetry into one or more than one line. For example, a circle can have an infinite number of symmetry lines as it can be folded from any diameter to make the symmetry line. Likewise, a square figure has four lines of symmetry, an equilateral triangle has three, a pentagon contains five and the hexagon has six lines of symmetry.
Also Read: Rotational Symmetry
Two Lines of Symmetry
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Two lines of Symmetry are defined as the figures that will divide the line of axis into two or more than two lines. For example, a rectangle has two lines of symmetry, this can be divided horizontally or vertically into two symmetrical lines. The two lines of symmetry are the combination of vertical, horizontal and diagonal lines.
Two lines of symmetry
This can be understood, if you can fold an A4 size paper vertically into two halves. Now after folding it vertically, fold it again in a horizontal position. After opening the page you will find that the page will contain two traces of lines both vertically and horizontally. This proves that the figure has two lines of symmetry.
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|---|---|---|
| Median of Triangle | Equation of a Line | Point of Intersection Formula |
Shapes with Two Lines of Symmetry
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Some of the geometrical that contains two lines of symmetry are given below
- Rectangle
- Rhombus
- English Alphabet H,I ,O and X
- An Hourglass
Things to Remember
- The symmetry of any object divides it into two equal mirror images. After splitting an object into two sides, both of its sides are exactly the same.
- Bilateral symmetry is defined as dividing a figure into two halves by only one line and they overlap with each other completely.
- There are four types of symmetry which are translation symmetry, rotational symmetry, reflection or reflexive symmetry and glide symmetry.
- A figure is said to be a line symmetry if any line can be drawn dividing it into two equal and symmetrical parts.
- A centre of symmetry is a point where symmetry exists when a figure is drawn around a single central point.
Also Read:
| Related Topics | |
|---|---|
| Coordinate System | Equation of a Plane |
| Straight Lines | Slope of Line |
Sample Questions
Ques. What do you mean by line symmetry? [2 marks]
Ans. At the point when a figure is folded along a line such a way that the two sections precisely fit on top of one another, then, at that point, the figure is said to have a line symmetry. Line of symmetry is the line that divides consider along with two indistinguishable parts and these are perfect mirror images of each other.
Ques. Does a square have 2 lines of symmetry? [2 marks]
Ans. For a square figure, it can be folded into one half over either diagonal, the horizontal segment of line that cuts the square into two equal halves, or in the vertical segments that will cut the square into two halves. Hence, the square has four lines of symmetry.
Ques. What is an example of a line of symmetry? [2 marks]
Ans. If we cut an apple in two equivalent parts, the piece of apple is supposed to be in symmetry with another. Another example is to suppose we cut a symmetrical triangle into equivalent parts, then, at that point, the two triangles framed after the convergence are the right-angled triangles.
Ques. Which triangle has two lines of symmetry? [2 marks]
Ans. There are no triangles that have two lines of symmetry. There are generally three different types of triangle in terms of the length of its sides i.e. equilateral, scalene and isosceles triangle. The equilateral triangle is a triangle that has three sides which are equal with each other and all the angles are equal to 60°. Hence, it will contain three lines of symmetry.
Ques. Which shape has no line of symmetry? [2 marks]
Ans. A scalene triangle, a parallelogram and a trapezium has only two of its sides are equal and the angles of all these geometrical shapes are not equal to each other. This is the reason these shapes have no lines of symmetry.
Ques. What is symmetry in alphabets?[2 marks]
Ans. Some of the English alphabets also show lines of symmetry. Horizontal symmetry is found in the letters of the alphabet such as B, C, D, E, H, I, K, O, and X. This means that the bottom of the letter of each of the letters is the reflection of the top. Apart from the letter, some horizontal symmetrical letters are BOX, BOOK, HIDE, CHEEK, BIKE, X-BOX.
Ques. Why does a rectangle have 2 lines of symmetry? [2 marks]
Ans. There are 2 symmetry lines of a rectangle which are from its length and breadth. These two lines may cut the rectangle in two similar halves which are mirror images of each other. If a rectangle can be folded along its line of symmetry, it superimposes perfectly.
Ques. Where are the lines of symmetry on a hexagon? [2 marks]
Ans. A hexagonal has 6 lines of Symmetry. 3 of those are the lines going through the mid marks of 2 opposite sides of the hexagon. and remaining 3 are the lines going through the opposite vertices of the hexagon. Apart from this, a regular hexagon also has rotational symmetry. Its angles of rotation is 60°.
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