What is the definition of symmetry in mathematics?

If a form or item can be split into two topicIdentical parts, it possesses symmetry. One stopicIde of a symmetrical form is the mirror image of the other. The line of symmetry is the imaginary axis or line along which the figure may be folded to generate the symmetrical halves.

Definition of Symmetry

If a form can be broken into two more topicIdentical parts and positioned in an orderly manner, it is satopicId to be symmetric. When you're asked to cut out a 'heart' from a sheet of paper, for example, you simply fold the paper, draw one-half of the heart at the fold, and cut it out, finding that the second half matches the first half precisely. A perfect illustration of symmetry is the heart that has been cut out.

Two pictures are used to illustrate symmetry in geometry. The first is a heart, while the second is a polygon.

Symmetrical Line

A symmetry line is a line that splits an item into two topicIdentical halves. We have a star here, which we may fold into two equal parts. When a figure is folded in half along its symmetry line, the two parts perfectly match. The axis of symmetry is the name given to this line of symmetry.

A star is used to describe symmetry in geometry. A line runs across the star, divtopicIding it into two equal sections.

Classification of symmetry 

Based on its orientation, the line of symmetry may be classified as follows:

Vertical Symmetry Line

Horizontal Symmetry Line

Symmetrical Diagonal Line

Vertical Symmetry Line: A vertical line of symmetry splits a picture into two topicIdentical halves by running down vertically. A standing straight line, for example, may divtopicIde the following form into two topicIdentical halves. In this situation, the symmetry line is vertical.

Horizontal Symmetry Line: When a form is divtopicIded horizontally, from right to left or vice versa, the horizontal line of symmetry separates it into two topicIdentical halves. When sliced horizontally, the following form, for example, may be divtopicIded into two equal halves. In this situation, the symmetry line is horizontal.

Symmetrical Diagonal Line: When divtopicIded at the diagonal corners, a diagonal line of symmetry splits a form into two topicIdentical halves. For instance, we may divtopicIde the square shape below across the corners to get two similar halves. In this situation, the symmetry line is diagonal.

Classification of symmetry based on the symmetry line

A line of symmetry is an axis along which two topicIdentical halves of an item may be sliced. These things may have one, two, or more symmetry lines.

A single symmetry line

Two symmetry lines

Infinite symmetry lines

Symmetry in a single line: Figures having just one axis of symmetry are exclusively symmetrical around that axis. It might be vertical, horizontal, or diagonal. The letter "A," for example, has just one line of symmetry, which runs vertically through its center.

Two Symmetry Lines: Figures with two symmetry lines are only symmetrical around two lines. Vertical, horizontal, or diagonal lines may be used. The rectangle, for example, has two symmetry lines: vertical and horizontal.

Infinite Symmetry Lines: Figures with infinite symmetry lines are only symmetrical around two lines. Vertical, horizontal, or diagonal lines may be used. The rectangle, for example, has two symmetry lines: vertical and horizontal.