## 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:**

- 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:**

- 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:

- 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:**

- M – has a vertical line of symmetry, O – has a vertical and horizontal line of symmetry. So, MOM has a vertical line of symmetry
- 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.
- 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:

- Find the line of symmetry in English alphabet letters.
- Find the rotational symmetry in English alphabet letters.
- Find the line of symmetry and rotational symmetry of the Semi-circle.
- Find the line of symmetry and rotational symmetry of the rectangle.
- Find the line of symmetry and rotational symmetry of the rhombus.
- Find the line of symmetry and rotational symmetry of the scalene triangle.
- 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.

#### Concept Map:

#### 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

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: