Class 7 Notes - Symmetry

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Symmetry

Symmetry is a fundamental concept in geometry that describes a situation where one shape becomes exactly like another when you move it in some way: turn, flip, or slide. In Class 7, students explore different types of symmetry, their properties, and their applications in mathematics and the real world.

1. Line Symmetry (Reflection Symmetry)

  • A figure has line symmetry if one half is a mirror image of the other half.
  • The line dividing the figure into two identical halves is called the line of symmetry.
  • Examples: Butterfly wings, human face, leaf, letters like A, M, T, H.
Example: Draw a line of symmetry for a square, rectangle, and equilateral triangle.

2. Number of Lines of Symmetry

  • Different shapes have different numbers of lines of symmetry.
  • Square: 4 lines of symmetry
  • Rectangle: 2 lines of symmetry
  • Circle: Infinite lines of symmetry
  • Equilateral triangle: 3 lines of symmetry
  • Isosceles triangle: 1 line of symmetry
  • Scalene triangle: No line of symmetry

3. Rotational Symmetry

  • A figure has rotational symmetry if it looks the same after a rotation (less than a full turn) about a point.
  • The number of times a figure matches itself in one full turn is called its order of rotational symmetry.
  • Examples:
    • Equilateral triangle: order 3
    • Square: order 4
    • Rectangle: order 2
    • Circle: infinite order
Example: Rotate a square by 90°, 180°, 270°, and 360°. It matches its original position 4 times.

4. Point Symmetry (Central Symmetry)

  • A figure has point symmetry if every part has a matching part at an equal distance from the central point but in the opposite direction.
  • Examples: Letter S, letter H, parallelogram.

5. Symmetry in Nature and Art

  • Butterflies, leaves, flowers, snowflakes, and starfish show symmetry.
  • Symmetry is used in architecture, rangoli, patterns, and designs.

6. Activities

  • Draw and cut out shapes. Fold them to find lines of symmetry.
  • Find objects around you that have symmetry.
  • Make rangoli or patterns using symmetrical designs.

7. Common Mistakes

  • Assuming all triangles have the same number of lines of symmetry.
  • Confusing rotational symmetry with line symmetry.
  • Missing lines of symmetry in regular polygons.

8. Practice Questions

  1. How many lines of symmetry does a regular pentagon have?
  2. Which of the following letters have line symmetry: A, B, C, D, E, H, K, M, N, O, S, T, U, V, W, X, Y, Z?
  3. Does a rectangle have rotational symmetry? If yes, what is its order?
  4. Draw a figure with point symmetry.
  5. Find three objects at home that have symmetry.

9. Summary

  • Symmetry makes objects balanced and beautiful.
  • There are different types of symmetry: line, rotational, and point.
  • Symmetry is found in nature, art, and everyday life.