How Many Lines of Symmetry

Introduction

If we are looking for the types of lines of symmetry, we have its count as three. On the other hand, if we are referring to the possible number of “lines of symmetry”, the range is from zero to infinity. Yes, we have geometric shapes that possess absolutely zero or no line of symmetry at all. On the contrary, there are cases where we get an infinite number of lines of symmetry. Isn't the concept of lines of symmetry interesting? We will learn here what it means by the term “lines of symmetry” and its characteristic features. Let's begin to gain deeper knowledge.

What is a Line of symmetry?

Well, the very word symmetry indicates something wish is similar or balanced or proportionate. When we are able to draw an imaginary line essentially passing through the center of any given geometric figure, such that the line divides the whole entity into two equal and similar (not almost similar) halves, we get a line of symmetry for that geometric figure.

A real-life example of the line of symmetry is the line passing through the diagonal of a square that divides the square into two equally sized triangles. Can we guess the type of these resulting triangles?

The Types of The Lines of symmetry

The following are the types of lines of symmetry.

• The Horizontal lines of symmetry

• The Vertical lines of symmetry

• The Diagonal lines of symmetry

The Properties of The Lines of symmetry

Here are some of the properties of the lines of symmetry.

• The lines of symmetry must pass through the center of the object or the figure.

• The minimum number of lines of symmetry that may exist is zero.

• The maximum number of lines of symmetry that can be drawn is literally infinite.

• The lines of symmetry dictate the classification of objects into the following two categories

• Symmetric Object

• Asymmetric Object

• Every line of symmetry splits the symmetrical object into two equal symmetric divisions.

Alternative Terms for The Lines of symmetry

We may come across several synonyms of the line of symmetry, some of which are as follows.

• Axis of symmetry

• Mirror Line

• Line of Reflection

The Count of The Lines of symmetry

We will explore here the range of the lines of symmetry with respect to some geometric shapes in the following way.

• The irregular geometric shapes have no line of symmetry.

• A few geometric shapes like the scalene triangles, the parallelogram, the trapezoids, etc. inherit zero lines of symmetry.

• The shapes with only one line of symmetry are the isosceles triangle, the isosceles trapezoid, etc.

• The shapes with two lines of symmetry are the rhombus, the rectangle, etc.

• An equilateral triangle is found to have three lines of symmetry.

• A square has four lines of symmetry of which one is the vertical line of symmetry, one is the horizontal line of symmetry and the rest two are the diagonal lines of symmetry.

• A regular pentagon exhibits five lines of symmetry.

• A regular hexagon displays six lines of symmetry.

• A regular heptagon shows seven lines of symmetry.

• A regular octagon presents eight lines of symmetry.

• A regular nonagon demonstrates nine lines of symmetry.

• A regular decagon manifests five lines of symmetry.

• The ultimate geometric figure supporting the infinite lines of symmetry is the circle because in the circle the lines of symmetry are along its diameter. As such we can have an infinite number of diameters of a circle.

Conclusion

• The lines of symmetry are applicable to objects or figures having two or more dimensions.

• Every Symmetric Object has at least one line of symmetry.

• An Asymmetric Object exhibits no lines of symmetry.

• A Horizontal line of symmetry is a line of symmetry that runs horizontally from the left-hand side to the right-hand-side or vice

• A Vertical line of symmetry traverses vertically from the down to the up direction or from the bottom to the top of the shape.

• Any Diagonal line of symmetry passes diagonally from one vertex to the other vertex joining the diagonal of the shape.

• The kite exhibits a single line of symmetry.

• The number of lines of symmetry that any n-sided regular polygon can have is equal to the number of sides of the n-sided regular polygon (which is n, where n is any positive integer).

• The number of lines of symmetry of any n-sided regular polygon is always less than the number of lines of symmetry of a circle.