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# Symmetry: Identification and Types of Symmetry

Aug 16, 2023

## Line Symmetry:

A figure in the plane has line symmetry if the figure can be mapped onto itself by a reflection in a line.

This line of reflection is a line of symmetry, such as the line ‘m’ at the right. A figure can have more than one line of symmetry.

Example:

1. Identify the lines of symmetry.

2. How many lines of symmetry does the object appear to have?

## Rotational Symmetry:

A figure in a plane has rotational symmetry if the figure can be mapped onto itself by a rotation of 180  or less about the center of the figure. This point is the center of symmetry. Note that the rotation can be either clockwise or counterclockwise.

For example, the figure below has rotational symmetry because a rotation of either 90° or 180°  maps the figure onto itself (although a rotation of 45°  does not).

The figure above also has point symmetry, which is 180° rotational symmetry.

For a figure with s lines of symmetry, the smallest rotation that maps the figure onto itself has the measure 360°/s

Examples:

1. Find the rotational symmetry of the equilateral triangle.

Solution:

An equilateral triangle has 3 sides.

Angle of rotation = 360°/3 = 120°

• Identify the line symmetry and rotational symmetry of the figure.

Solution:

The above figure does not have line symmetry and it has 90° rotational symmetry.

#### Examples:

1. Identify the line symmetry and rotational symmetry of the figure.

Solution:

The above figure is a square, which has 4 equal sides.

Line symmetry – it has four lines of symmetry

Rotational symmetry – 90°

• Identify the line symmetry and rotational symmetry (if any) of each word.
• MOM
• OX

Solution:

1. M – has a vertical line of symmetry, O – has a vertical and horizontal line of symmetry. So, MOM has a vertical line of symmetry
2. O- has a vertical and horizontal line of symmetry and X- has a horizontal and vertical line of symmetry. But OX has a horizontal line of symmetry.
3. Identify the line symmetry and rotational symmetry of the figure.

Solution:

The above-given figure is an equilateral triangle, it has 3 equal sides.

Line of symmetry – 3 lines of symmetry

Rotational symmetry – 120°

#### Exercise:

1. Find the line of symmetry in English alphabet letters.
2. Find the rotational symmetry in English alphabet letters.
3. Find the line of symmetry and rotational symmetry of the Semi-circle.
4. Find the line of symmetry and rotational symmetry of the rectangle.
5. Find the line of symmetry and rotational symmetry of the rhombus.
6. Find the line of symmetry and rotational symmetry of the scalene triangle.
7. Find the line of symmetry and rotational symmetry of the parallelogram.

8. Find line of symmetry and rotational symmetry of the figure.

9. Find line of symmetry and rotational symmetry of the figure.

10. Find line of symmetry and rotational symmetry of the figure.

#### What We Have Learned:

• Understand and identify line symmetry
• Understand and identify lines of symmetry
• Understand and identify rotational symmetry
• Understand and identify the center of rotation

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