Line Symmetry
“Line symmetry means folding makes both halves match.”
The hook
A butterfly, a heart, a face — fold down the middle and both halves land right on top of each other.
In plain words
The property that folding along a line (the axis) makes the two halves match exactly.
The intuition
Draw a shape and fold the paper in half. If the left and right match like a mirror along the crease, it has line symmetry. That crease is the axis, and every point has a partner the same distance across.
How it's built
A shape can have one axis or many. A square has 4, a non-square rectangle has 2, a circle has countless. To find an axis, look for a fold line that makes the halves overlap.
Example
A non-square rectangle folds to match once across and once down — it has 2 axes of symmetry.
Common mistake
Folding along a diagonal does not always match. A rectangle folded on its diagonal comes out crooked — that line is not an axis.
Where it's used
Balance in design, logos, and buildings; making patterns; recognizing letters and shapes.
Where it came from
Balanced symmetry appears in nature — butterflies, flowers, snowflakes — and has long been a mark of beauty in art and architecture.
Quick check
How many axes of symmetry does a square have?
- 1
- 2
- 4✓
- 0
Practice
How many axes of symmetry does a non-square rectangle have?
Answer: 2
- Fold across the middle → matches
- Fold down the middle → matches
- Diagonals don't → 2 axes
Takeaway: A rectangle has 2 axes of symmetry.
How many axes of symmetry does an equilateral triangle have?
Answer: 3
- From each corner to the middle of the opposite side
- 3 corners → 3 axes
Takeaway: Equal sides give more axes.
Draw a heart, fold it in half, and mark where the axis of symmetry is in your notebook.
Answer: undefined
- Fold the heart down the middle and the halves match.
- That vertical line is the axis.
- A heart has 1 axis.
Takeaway: The fold that makes halves match is the axis.