Symmetry (NCERT Ch. 13)

• Identify figures with line symmetry (also called reflection symmetry or mirror symmetry).
• Find the number of lines of symmetry in common shapes.
• Relate symmetry to mirror reflection.

1. A figure has line symmetry if it can be folded along a line so the two halves match exactly.
2. This fold line is called the line of symmetry (or axis of symmetry).
3. A figure can have no, one, or many lines of symmetry.
4. A circle has infinite lines of symmetry (any diameter works).
5. A regular polygon with n sides has exactly n lines of symmetry.
6. Mirror reflection produces a symmetric (left-right reversed) image about the mirror line.

How many lines of symmetry does a square have?

A square has 4 lines of symmetry: 2 through opposite vertices (diagonals)
and 2 through midpoints of opposite sides.

• Assuming every closed shape is symmetric — many irregular shapes have zero lines of symmetry.
• Confusing rotational symmetry with line symmetry (line symmetry needs a fold/mirror line).
• Miscounting lines of symmetry in regular polygons (it always equals the number of sides).

• How many lines of symmetry does an equilateral triangle have?
• Does the letter "F" have a line of symmetry?

Open the Practice tab for graded questions on Symmetry (NCERT Ch. 13).