Chapter 12: Symmetry and Patterns

Introduction

• Teacher: Poonam Divyadi
• Overview of topics covered:
  • Symmetry and Line of Symmetry
  • Symmetry in Plane Shapes
  • Symmetry in Alphabet
  • Reflection Symmetry
  • Rotational Symmetry
  • Tessellation
  • Patterns

1. Symmetry

• Definition: A figure is symmetrical if divided into two equal halves of the same shape and size.
• Line of Symmetry: The line that divides a figure into two equal parts.
• Example: A tree figure can be folded along the line of symmetry to show overlapping sides.

2. Symmetry in Plane Shapes

A. Square

• Has 4 lines of symmetry:
  1. Horizontal
  2. Vertical
  3. Two Slanting (diagonal) lines

B. Rectangle

• Has 2 lines of symmetry:
  1. Horizontal
  2. Vertical

C. Triangle

• Types:
  1. Equilateral Triangle:
     • 2 lines of symmetry (1 vertical and 2 slanting)
  2. Isosceles Triangle:
     • 1 line of symmetry (vertical)
  3. Scalene Triangle:
     • No line of symmetry

D. Circle

• Has infinite lines of symmetry (can be divided at any angle)
• Example: Ashoka Chakra with 24 spokes.

3. Symmetry in Alphabet

A. Horizontal Line of Symmetry

• Letters: B, C, D, E, K (divided horizontally)

B. Vertical Line of Symmetry

• Letters: A, M, T, U (divided vertically)

C. Two Lines of Symmetry

• Letters: H, I, X, O (can be folded both horizontally and vertically)

D. No Line of Symmetry

• Letters: F, G, J, L (no overlapping when folded)

4. Reflection Symmetry

• Definition: An image looks the same on either side of a line.
• Example: Half of an object can be mirrored to create the other half.

5. Rotational Symmetry

• Definition: The number of times an object looks the same while rotated in one full turn.
• Example: Duster rotated at various degrees (90°, 180°, 270°, and back to original).

6. Nets

• Definition: A two-dimensional shape that can be folded to form a three-dimensional shape.
• Example: Cube (6 faces, 8 vertices, 12 edges).

7. Tessellation

• Definition: A design that fits together without gaps or overlaps.
• Example: A figure that completely fills a plane without gaps.

8. Patterns

• Definition: A sequence of repeated numbers, shapes, or objects.
• Example: A pattern of even numbers (2, 4, 6, 8, ...).

Conclusion

• Summary of key concepts in symmetry and patterns.
• End of Chapter 12.