2D shapes
Symmetry
In this section you find all the lines of symmetry in 2D shapes and patterns, including vertical, horizontal and diagonal lines.
What a line of symmetry is
If a shape can be folded in half exactly onto itself along a line, then that line is a line of symmetry. The two halves match ā they are mirror images of each other. One line of symmetry splits a shape into 2 equal halves.
Vertical, horizontal and diagonal lines
A line of symmetry can be vertical (straight up and down), horizontal (straight across, side to side) or diagonal (slanting from corner to corner). When you look for lines of symmetry, check for a vertical line, a horizontal line and the two diagonal lines. You can use a mirror or fold the shape to check.
Lines of symmetry in shapes
Different shapes have different numbers of lines of symmetry: ā¢ a rectangle has 2 (one vertical, one horizontal). ā¢ an equilateral triangle has 3. ā¢ a square has 4. A slanted parallelogram whose sides are not all equal has no lines of symmetry.
Regular polygons
For a regular polygon, the number of lines of symmetry is equal to the number of sides. So a regular pentagon has 5 lines of symmetry, a regular hexagon has 6, and a regular octagon has 8.
Worked examples
Folding to find a line of symmetry
- Fold the shape in half along a line.
- Check whether the two halves match exactly.
- If they do, the fold is a line of symmetry.
Answer: A matching fold is a line of symmetry.
Lines of symmetry on a square
- Fold the square top to bottom and side to side ā both match.
- Fold along each diagonal ā both match too.
- Count all the folds that match.
Answer: A square has 4 lines of symmetry.
Lines of symmetry on a rectangle
- Fold the rectangle top to bottom ā the halves match.
- Fold it side to side ā the halves match.
- Try the diagonals ā they do not match, so do not count them.
Answer: A rectangle has 2 lines of symmetry.
Lines of symmetry on a regular polygon
- Count the sides of the regular polygon.
- A regular octagon has 8 sides.
- The number of lines of symmetry equals the number of sides.
Answer: A regular octagon has 8 lines of symmetry.
Where you see this in real life
- A butterfly's wings match on both sides of a vertical line of symmetry.
- Symmetrical patterns in tiles, fabric and art and design.
- Snowflakes and flowers that look the same on each side of a line.
Key words
- Symmetry
- When two halves of a shape are mirror images of each other.
- Line of symmetry
- A line that folds a shape into two matching halves.
- Vertical
- Going straight up and down.
- Horizontal
- Going straight across, from side to side.
- Diagonal
- A slanting line, such as from one corner to another.
- Regular polygon
- A polygon with all sides the same length, whose number of lines of symmetry equals its number of sides.