Symmetry

Key notes :

1. Definition of Symmetry:

  • Symmetry refers to a balanced and proportionate similarity found in two halves of an object, where one half mirrors the other.
  • A figure is said to be symmetric if it can be divided into two identical parts.

2. Line of Symmetry:

  • A line of symmetry divides a figure into two identical halves.
  • A shape can have more than one line of symmetry, depending on its structure.
  • For example, a square has 4 lines of symmetry, while a rectangle has 2.

3. Types of Symmetry:

  • Line Symmetry (Reflectional Symmetry): A figure has line symmetry if one half is a mirror image of the other.
  • Rotational Symmetry: A figure has rotational symmetry if it looks the same after a certain amount of rotation (less than a full turn).
    • Order of Rotation: The number of times a shape looks the same during a full 360° rotation. For example, an equilateral triangle has rotational symmetry of order 3.

4. Examples of Symmetry in Geometry:

  • Equilateral Triangle: Has 3 lines of symmetry and rotational symmetry of order 3.
  • Square: Has 4 lines of symmetry and rotational symmetry of order 4.
  • Circle: Infinite lines of symmetry and rotational symmetry of any angle.

Learn with an example

🔔 Is the dotted line a line of symmetry?

  • yes
  • no

Imagine folding this picture along the dotted line.

The two sides will not match up. The dotted line is not a line of symmetry.

Now try folding along this dotted line instead. This dotted line is a line of symmetry.

🔔 Is the dotted line a line of symmetry?

  • yes
  • no

Imagine folding this picture along the dotted line.

The two sides will not match up. The dotted line is not a line of symmetry.

🔔 Is the dotted line a line of symmetry?

  • yes
  • no

Imagine folding this picture along the dotted line.

The two sides will match up exactly. The dotted line is a line of symmetry.

Let’s practice!🖊️