Symmetry Line Plane Shapes

Introduction to Symmetry Line Plane Shapes

Symmetry is In all over the world, from the human face to the wonders of the world, Symmetry is spread out everywhere. It's just a matter of observing things around us. it’s called Fractals. Symmetrics are useful in the field arts and designing fields. Here we’ll discuss lines of symmetry of plane shapes and Let's get deeper into symmetry line plane shapes.

 

Definition: A line of symmetry is a line along which the plane or shape is divided into two equal parts. In other words, a line of symmetry divides a plane or shape into halves. For example: Observe the white line in the following image. It divides the dog face into two equal halves. Also, these two halves are mirror images of each other.

 

How to Find Symmetry Line Plane Shapes?

Although, identifying how many lines of symmetry a plane shape has is not very difficult nonetheless folding method is the popular and easiest method to do so. 

 

Folding Test

As the name suggests, we can find the line of symmetry by just folding the plane and shapes. After getting folded if the plane exactly overlaps on the other part then the folded line is the line of symmetry.

 

Example: In the following diagram we have folded the rectangle along a vertical line. Observe the folded part we represented on the right side. It exactly overlaps the other part. So the vertical line is our line of symmetry.

If we have folded the rectangle along with any of the diagonal lines then it’ll not overlap on the other side. As shown in the following image. And hence It’ll not be the line of symmetry.

 

Lines of Symmetry of Plane Shapes

  • Triangle

We know that any shape which is closed by three sides, is called a triangle. The triangles can be divided into three parts. 

 

1. Equilateral Triangle: A triangle with all sides and angles are equal is called an equilateral triangle. In these triangles, there are a total of 3 lines of symmetry as shown below.

2. Isosceles Triangle: A triangle with two sides and angles that are equal is called the Isosceles triangle. In these triangles, there is only 1 line of symmetry as shown below.

3. Scalene Triangle: A triangle in which no sides and angles are equal is called a scalene triangle. In these triangles, there is no line of symmetry because we can not divide such triangles into equal halves. as shown below.

  • Quadrilaterals

We know that any shape which is closed by four sides, is called a Quadrilaterals. We’ll see the line of symmetry in quadrilaterals as followers:

 

1. Square: A square is a parallelogram with all sides and angles are equal. Since all angles are equal, it is just an easy calculation to get each angle as $90^{\circ}$. There are 4 lines of symmetries in a square which can be seen as follows:

2. Rectangle: A rectangle is a parallelogram with opposite sides equal and parallel and all angles are equal. Since all angles are equal, it is just an easy calculation to get each angle as $90^{\circ}$. There are 2 lines of symmetries in the rectangle which can be seen as follows:

3. Rhombus: A rhombus is a quadrilateral with all sides of equal length. There is 2 line of symmetry in rhombus which can be seen as follows:

4. Kite: A Kite is simply a kite-shaped quadrilateral. It has only 1 line of symmetry.

5. Irregular Quadrilateral: An irregular quadrilateral is a quadrilateral with no proper geometry. It is just closed with four sides. It has no line of symmetry.

  • Regular Shapes

A regular shape is a plane shape with all sides and angles are equal. It is divided on a number of sides. 

  1. If the number of sides is 3 then it’s called an equilateral triangle. We have already discussed it earlier. It has 3 lines of symmetry.

  2. If the number of sides is 4 then it’s called square. We have already discussed it earlier. It has 4 lines of symmetry.

  3. If the number of sides is 5 then it’s called a regular pentagon. It has 5 lines of symmetry.

  1. If the number of sides is 6 then it’s called a regular hexagon. It has 6 lines of symmetry.

  1. If the number of sides is 7 then it’s called a regular heptagon. It has 7 lines of symmetry. 

  1. If the number of sides is 8 then it’s called a regular octagon. It has 8 lines of symmetry.

Note: With the same above pattern a polygon with n sides will have n lines of symmetry.

 

Did you know:

  • A circle has infinite lines of symmetry.

  • There are four types of symmetry as follows:

    1. Translational symmetry

    2. Rotational symmetry

    3. Reflectional symmetry

    4. glide reflection

  • Shapes that are not symmetrical are called asymmetric.

FAQs (Frequently Asked Questions)

1. What Can We Say about Symmetrical Shapes?

Ans: A shape is called symmetric if it has at least one line of symmetry. For example, a kite has only one line of symmetry.

2. What are the types of symmetry?

Ans: Symmetry can be divided into 4 types: 


A. Translational Symmetry: Let us suppose that an object is moving either forward or backward. If its movement occurs with a pattern. Then such a pattern is called translational symmetry. For example the movement of a particle on a sine curve. 


B. Rotational Symmetry: Let us suppose that an object is rotating in a particular direction, around an axis then it is called rotational symmetry. For example Rotation of the earth on its axis.


C. Reflexive Symmetry: It’s also called mirror symmetry. It is a type of symmetry where one half of the object is a mirror image of the other half part. 


D. Glide Symmetry: Glide symmetry is the combination of both translation and reflection transformations.

3. What Do You Mean by Point Symmetry?

Ans: If a shape is looking the same when we turn it upside down and matching parts are in the opposite direction then we call such symmetry as point Symmetry.

4. How Many Lines of Symmetry a Regular Polygon Have?

Ans. A regular polygon has n number of sides with all sides and angles are equal. Depending on the number of sides, a regular polygon has n number of lines of symmetry if it has n sides.