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.
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 Plane Shapes
1. What is a line of symmetry in a plane shape?
A line of symmetry is an imaginary line that divides a plane shape into two identical halves, where each half is the perfect mirror image of the other. If you were to fold the shape along this line, the two parts would overlap exactly.
2. How many lines of symmetry do common quadrilaterals like a square and a rectangle have?
The number of lines of symmetry varies for different quadrilaterals based on their properties:
- A square has 4 lines of symmetry: two that connect the midpoints of opposite sides and two that run through opposite vertices (diagonals).
- A rectangle has only 2 lines of symmetry: the lines that connect the midpoints of its opposite sides.
- A rhombus also has 2 lines of symmetry, which are its diagonals.
3. How do the lines of symmetry differ between an equilateral, isosceles, and scalene triangle?
The difference in lines of symmetry for triangles is based on the equality of their sides and angles:
- An equilateral triangle, with all three sides equal, has 3 lines of symmetry. Each line passes through a vertex and the midpoint of the opposite side.
- An isosceles triangle, with two equal sides, has only 1 line of symmetry, which bisects the angle between the two equal sides.
- A scalene triangle, with no equal sides, has 0 lines of symmetry as it cannot be divided into two identical halves.
4. What is the general rule for finding the number of lines of symmetry in any regular polygon?
For any regular polygon (a shape with all sides and all angles equal), the number of lines of symmetry is equal to its number of sides. For example, a regular pentagon has 5 sides and 5 lines of symmetry, and a regular octagon has 8 sides and 8 lines of symmetry.
5. Which capital letters in the English alphabet show line symmetry?
Many capital letters have lines of symmetry. They can be categorised as follows:
- Vertical line of symmetry: A, H, I, M, O, T, U, V, W, X, Y
- Horizontal line of symmetry: B, C, D, E, H, I, K, O, X
- Letters like H, I, O, and X have both horizontal and vertical lines of symmetry.
6. Why is the diagonal of a rectangle not considered a line of symmetry?
A diagonal of a rectangle is not a line of symmetry because if you fold a rectangular paper along one of its diagonals, the two halves do not overlap exactly. The vertices of the folded parts will not align with each other, which proves that the diagonal does not create two mirror-image halves.
7. What is the main difference between line symmetry and rotational symmetry?
The main difference lies in the transformation applied. Line symmetry (or reflectional symmetry) is when a shape looks the same after being flipped over a line. In contrast, rotational symmetry is when a shape looks the same after being rotated less than a full 360 degrees around a central point.
8. Why does a circle have infinite lines of symmetry?
A circle has infinite lines of symmetry because any line that passes through its centre will divide it into two identical semicircles (mirror images). Since an infinite number of such lines (diameters) can be drawn through the centre of a circle, it is considered to have an infinite number of symmetry lines.
9. Can a shape have no lines of symmetry at all? Provide some examples.
Yes, many shapes have no lines of symmetry. These are called asymmetrical shapes. Common examples in geometry include a scalene triangle (where all sides are different lengths) and an irregular quadrilateral (a four-sided shape with no specific properties of symmetry).
10. How is the concept of symmetry in plane shapes applied in the real world?
Understanding symmetry is crucial in many real-world fields. For example:
- In art and design, symmetry is used to create balance, harmony, and aesthetically pleasing patterns.
- In architecture, symmetrical designs are used for stability and visual appeal in buildings and bridges.
- In nature, most animals exhibit bilateral symmetry, and many flowers and snowflakes show radial symmetry.
- In engineering, symmetry is fundamental to designing balanced and functional components, from car wheels to aircraft wings.
