What is Symmetry Class 7 Maths: Definition and Examples

Definition of Symmetry in Class 7 Maths

Symmetry is when a figure or shape looks exactly the same after a certain operation, such as folding or turning. In Class 7 NCERT maths, symmetry mainly refers to line symmetry and rotational symmetry.

• Line Symmetry (Reflection Symmetry): A shape has line symmetry if it can be divided by a line (called the line of symmetry) into two identical halves that are mirror images.
• Rotational Symmetry: A shape has rotational symmetry if it can be rotated (less than a full turn) around a point and still look the same.

For example, a square has 4 lines of symmetry and rotational symmetry of order 4 because it looks the same after rotating 90°, 180°, 270°, and 360°.

Understanding this definition helps students identify symmetric shapes and solve related problems in exams.

Types of Symmetry Explained with Examples

In Class 7 maths, you will mainly study two types of symmetry:

1. Line Symmetry: When a figure can be folded along a line so that both halves match perfectly.

• Example: A butterfly’s wings, the English alphabet 'A', or a circle.

2. Rotational Symmetry: When a figure can be rotated about its center and still appear unchanged.

• Example: A star, a square, or the letter 'S'.

Here is a comparison table to help you understand better:

Recognizing these types helps in identifying symmetry in various shapes and patterns.

How to Identify Line Symmetry in Shapes

To identify line symmetry in any shape, follow these steps:

• Step 1: Imagine folding the shape along a line.
• Step 2: Check if both parts match exactly.
• Step 3: If they match, the line is called the line of symmetry.

For example, consider a rectangle:

• A rectangle has 2 lines of symmetry — one vertical and one horizontal.

Worked Example:

Find the number of lines of symmetry in an equilateral triangle.

• An equilateral triangle has 3 equal sides.
• It has 3 lines of symmetry, each passing through a vertex and the midpoint of the opposite side.

This method helps you quickly find lines of symmetry in any figure.

Understanding Rotational Symmetry with Formula

Rotational symmetry means a shape looks the same after being rotated by a certain angle less than 360°.

• The order of rotational symmetry is the number of times the shape matches itself during one full rotation (360°).

Formula:

$$ \text{Angle of rotation} = \frac{360^\circ}{\text{Order of rotational symmetry}} $$

Example:

A square has rotational symmetry of order 4.

• Angle of rotation = $\frac{360^\circ}{4} = 90^\circ$

This means the square looks the same after rotating 90°, 180°, 270°, and 360°.

Knowing this formula helps you solve problems involving rotational symmetry efficiently.

Importance of Symmetry in Class 7 NCERT Maths Exams

Symmetry is an important topic in Class 7 NCERT maths because:

• It develops spatial understanding and visualization skills.
• Many geometry problems are based on symmetry concepts.
• Questions on symmetry often appear in CBSE exams.
• Practicing symmetry helps in solving complex problems easily.

To prepare well:

• Study definitions and properties carefully.
• Practice all exercises given in the NCERT textbook.
• Draw diagrams to understand symmetry visually.
• Solve previous year question papers focusing on symmetry questions.

This approach ensures strong conceptual clarity and exam readiness.

Solved Example: Finding Lines of Symmetry

Example: How many lines of symmetry does the letter 'H' have?

Solution:

• The letter 'H' is symmetrical vertically and horizontally.
• It has 2 lines of symmetry:
• One vertical line through the middle.
• One horizontal line through the middle.

Therefore, the letter 'H' has 2 lines of symmetry.

Try practicing with other letters and shapes to master this skill.