Mathematics Class 7 - Symmetry Notes

Symmetry

Welcome to the chapter on Symmetry for Class 7. In this chapter, you will learn what symmetry means, how to identify symmetrical shapes, and how symmetry is used in mathematics and the world around us. By the end of this chapter, you will be able to recognize and draw lines of symmetry and understand rotational symmetry!

Introduction

Symmetry is when one shape becomes exactly like another if you flip, slide, or turn it. Symmetrical objects look the same on both sides of a line or around a point.

Line of Symmetry

A line of symmetry divides a figure into two identical parts. Each part is a mirror image of the other.

• A square has 4 lines of symmetry.
• A rectangle has 2 lines of symmetry.
• A circle has infinite lines of symmetry.
• Some shapes, like a scalene triangle, have no lines of symmetry.

Rotational Symmetry

Rotational symmetry means a shape looks the same after being rotated (turned) by a certain angle.

• A square has rotational symmetry of order 4 (it looks the same after 90°, 180°, 270°, and 360° turns).
• An equilateral triangle has rotational symmetry of order 3.

Examples of Symmetry in Nature and Art

• Butterfly wings are symmetrical.
• Leaves, flowers, and snowflakes show symmetry.
• Many designs and patterns in art use symmetry.

How to Check for Symmetry

• Fold the shape along a line. If both halves match, it is a line of symmetry.
• Rotate the shape to see if it matches its original position.

Fun Activity: Symmetry Hunt!

Look for symmetrical objects at home or outside. Draw them and mark their lines of symmetry!

Summary

• Symmetry means two parts are the same.
• Line of symmetry divides a shape into mirror images.
• Rotational symmetry means a shape looks the same after turning.
• Symmetry is found in nature, art, and mathematics.

Practice Questions

1. How many lines of symmetry does a rectangle have?
2. Name a shape with no line of symmetry.
3. What is rotational symmetry?
4. Draw a shape with 3 lines of symmetry.
5. Give an example of symmetry in nature.

Challenge Yourself

• Find and draw a pattern with both line and rotational symmetry.
• Make a paper snowflake and count its lines of symmetry.

Did You Know?

• The Taj Mahal is famous for its beautiful symmetry!
• Many animals, like starfish, show rotational symmetry.

Glossary

• Symmetry: When two parts are the same.
• Line of Symmetry: A line that divides a shape into two equal parts.
• Rotational Symmetry: When a shape looks the same after turning.
• Order of Symmetry: The number of times a shape matches itself in one full turn.

Answers to Practice Questions

1. 2
2. Scalene triangle
3. When a shape looks the same after being rotated by a certain angle.
4. Equilateral triangle
5. Butterfly wings, leaves, flowers, snowflakes

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Notice symmetry around you and use it to make beautiful designs!