How to Find the Line of Symmetry in 2D Plane Shapes with Properties and Solved Examples
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.
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.
If the number of sides is 4 then it’s called square. We have already discussed it earlier. It has 4 lines of symmetry.
If the number of sides is 5 then it’s called a regular pentagon. It has 5 lines of symmetry.
If the number of sides is 6 then it’s called a regular hexagon. It has 6 lines of symmetry.
If the number of sides is 7 then it’s called a regular heptagon. It has 7 lines of symmetry.
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:
Translational symmetry
Rotational symmetry
Reflectional symmetry
glide reflection
Shapes that are not symmetrical are called asymmetric.
FAQs on Symmetry Line in Plane Shapes Explained with Clear Examples
1. What is a symmetry line in plane shapes?
A symmetry line (or line of symmetry) is a line that divides a plane shape into two identical mirror-image halves. When a shape is folded along this line, both halves match exactly. This concept is also called reflection symmetry in geometry. For example, a square has lines that split it into equal mirrored parts, showing perfect symmetry.
2. How do you find the line of symmetry of a shape?
To find a line of symmetry, check whether a line can divide the shape into two equal mirror-image halves.
- Step 1: Visualize or draw a line through the shape.
- Step 2: Fold the shape along that line (mentally or physically).
- Step 3: If both halves match exactly, the line is a symmetry line.
3. How many lines of symmetry does a square have?
A square has 4 lines of symmetry. These include:
- 2 lines through the midpoints of opposite sides (vertical and horizontal).
- 2 diagonal lines joining opposite vertices.
4. How many lines of symmetry does a rectangle have?
A rectangle has 2 lines of symmetry. These are:
- One vertical line through the center.
- One horizontal line through the center.
5. How many lines of symmetry does a triangle have?
The number of lines of symmetry in a triangle depends on its type.
- Equilateral triangle: 3 lines of symmetry.
- Isosceles triangle: 1 line of symmetry.
- Scalene triangle: 0 lines of symmetry.
6. How many lines of symmetry does a circle have?
A circle has infinitely many lines of symmetry. Every line passing through the center (diameter) divides the circle into two identical halves. Since there are infinitely many diameters, there are infinitely many symmetry lines.
7. What is the difference between line symmetry and rotational symmetry?
The difference is that line symmetry involves reflection across a line, while rotational symmetry involves turning around a fixed point.
- Line symmetry: The shape matches when folded along a line.
- Rotational symmetry: The shape matches after rotating by a certain angle less than 360°.
8. What is the formula for the number of lines of symmetry in a regular polygon?
A regular polygon with n sides has n lines of symmetry. This means:
- An equilateral triangle (n = 3) has 3 lines.
- A square (n = 4) has 4 lines.
- A regular pentagon (n = 5) has 5 lines.
9. Can a shape have no line of symmetry?
Yes, a shape can have no line of symmetry if it cannot be divided into two identical mirror halves. Examples include:
- A scalene triangle.
- An irregular quadrilateral.
- Any uneven or distorted shape.
10. Why is symmetry important in geometry and real life?
Symmetry is important because it helps identify balance, structure, and patterns in plane shapes and real-world objects. In geometry, symmetry simplifies problem-solving and classification of shapes. In real life, symmetry appears in:
- Architecture and building design.
- Art and logos.
- Nature (butterflies, flowers).
