The Axis of symmetry applies to any object or figure we see in the real world. It is an imaginary line that divides an object into two halves that are identical to each other. In other words, an axis of symmetry creates a mirror-like reflection on either side of the object along the axis of symmetry. Symmetry is an important concept in geometry that divides a figure into two halves that are exact reflections of each other.

The axis of symmetry divides a shape into two identical parts. It means if we consider folding the figure along the axis of the symmetry, the two parts get exactly superimposed. A shape can have one or more than one axis of symmetry. Different shapes can have a different number of lines of symmetry.

A square has four axes of symmetry. Two of them bisect the sides and divide the square into two equal rectangular parts. The other two pass through the corners and divide the square into two equal triangular parts.

• A rectangle has two axes of symmetry bisecting the sides.
• A rhombus has two axes of symmetry as two diagonals. 
• A circle has an infinite number of axes of symmetry because each diameter is an axis of symmetry.
• An equilateral triangle has three axes of symmetry passing through the vertices.

A parabola has only one line of symmetry. It passes through the vertex of the parabola. If a parabola opens up or down and has a vertex as (a, b) then the equation of the axis of symmetry is x=a. If the parabola opens on the left or right and it has a vertex as (a,b) then the equation of the axis of symmetry is y=b.

Not all shapes need to have an axis of symmetry. A parallelogram doesn’t have any axis of symmetry.

Line of Symmetry

The line of symmetry can be vertical, horizontal, or slanting depending on the shape of the object. On a coordinate plane, the axis of symmetry is parallel to the x-axis when it is horizontal and it is vertical when it is parallel to the y-axis. Any axis of symmetry that creates a slope with an x-axis is considered a slanting axis of symmetry. 

We can consider the lines of symmetry for objects that we see in real life like flowers, leaves, insects, buildings, monuments, etc. which normally have a vertical axis of symmetry. It is also applicable to various letters like M, A, H, T, etc. that have a vertical axis of symmetry.

The rotational symmetry of order n means a shape when rotated by an angle that is equal to 360 degrees divided by n; the shape repeats itself or doesn’t change the shape. Regular polygons have a degree of rotational symmetry equal to 360 degrees divided by several sides. Regular polygons have many axes of symmetry which is equal to the number of sides.

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