Symmetry

Symmetry is a property where one shape becomes exactly like another when you move it in some way: turn, flip, or slide. In mathematics, symmetry usually refers to mirror (or reflectional) symmetry.

1. Line of Symmetry

A line of symmetry divides a figure into two identical parts that are mirror images of each other. This line is also called the axis of symmetry.

• A square has 4 lines of symmetry.
• A rectangle has 2 lines of symmetry.
• A circle has infinite lines of symmetry.
• Some shapes, like the letter "A", have 1 line of symmetry.

2. Identifying Symmetrical Figures

• Draw a line through the center of a shape. If both sides match exactly, the shape is symmetrical.
• Common symmetrical shapes: square, rectangle, circle, equilateral triangle.
• Some shapes, like a scalene triangle, have no lines of symmetry.

3. Reflection and Mirror Images

When a shape is reflected over a line of symmetry, the image looks exactly like the original shape but reversed. This is called a mirror image.

• Folding a paper along the line of symmetry shows if the two halves match.
• Mirror images are used in art, design, and nature (e.g., butterfly wings).

4. Rotational Symmetry

A shape has rotational symmetry if it looks the same after a certain amount of rotation (less than a full turn).

• A square has rotational symmetry of order 4 (it matches itself 4 times in a full turn).
• A rectangle has rotational symmetry of order 2.
• A circle has infinite rotational symmetry.

5. Symmetry in Nature and Daily Life

• Butterflies, leaves, and flowers often show symmetry.
• Human faces and bodies have approximate symmetry.
• Many buildings and designs use symmetry for beauty and balance.

6. Activities

• Draw lines of symmetry on different shapes (triangle, square, rectangle, pentagon, etc.).
• Find objects at home or school that are symmetrical.
• Fold paper to check for symmetry.
• Make symmetrical patterns using colors or blocks.

7. Practice Questions

1. How many lines of symmetry does a regular hexagon have?
2. Draw the lines of symmetry for the letter "H".
3. Which of these shapes has no line of symmetry: triangle, circle, scalene triangle?
4. Does the number 8 have symmetry? If yes, how many lines?
5. Give two examples of symmetry in nature.

8. Summary

• Symmetry means both sides are identical when divided by a line (mirror symmetry).
• Rotational symmetry means a shape looks the same after rotation.
• Symmetry is found in shapes, letters, numbers, nature, and designs.