Symmetrical Designs — Lines of Symmetry and Mirror Images
Have you noticed that a butterfly's wings look the same on both sides? That is symmetry! When one half of a shape is a mirror image of the other half, the shape is called symmetrical.
Line of Symmetry
A line of symmetry (also called a mirror line) divides a shape into two equal halves that match exactly when folded. A shape can have one, two, many, or no lines of symmetry.
- An equilateral triangle has 3 lines of symmetry.
- A square has 4 lines of symmetry.
- A rectangle (non-square) has 2 lines of symmetry.
- A circle has infinitely many lines of symmetry.
- The letter A has 1 line of symmetry.
Mirror Image
When you hold a shape next to a mirror, the reflection you see is its mirror image. The image is the same size but flipped.
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Draw a line of symmetry for the letter M.
The vertical line down the centre of M divides it into two equal halves. M has 1 line of symmetry.
How many lines of symmetry does a regular hexagon have?
A regular hexagon has 6 lines of symmetry — 3 through opposite corners and 3 through midpoints of opposite sides.
Is the letter Z symmetrical?
The letter Z has no line of symmetry (neither vertical nor horizontal fold gives matching halves).
A rangoli pattern is made of 4 identical petals arranged equally. How many lines of symmetry does it have?
There are 4 lines of symmetry, one through each petal.
A paper is folded in half and a half-heart is cut. When unfolded, what shape appears?
A full heart — the fold was the line of symmetry.
Common mistakes
- Thinking every shape has only one line of symmetry.
- Confusing rotation with reflection — a mirror image is a flip, not a turn.
Summary
A symmetrical shape has at least one line of symmetry. Fold or use a mirror to check. Designs in art, nature, and buildings often use symmetry to look balanced and beautiful.