Pattern & symmetry
Shape and symmetry
A symmetrical shape can be split along a line of symmetry into two equal halves that are mirror images of each other.
What symmetry means
A line of symmetry splits a shape into two equal halves. Each half is a mirror image of the other. The line of symmetry is also called the mirror line.
Vertical and horizontal lines
A line of symmetry can be vertical (going straight up and down) or horizontal (going straight across, side to side). Some shapes have both.
Lines of symmetry in shapes
Different shapes have different numbers of lines of symmetry: ā¢ a rectangle has 2 (one vertical, one horizontal). ā¢ a square has 4. ā¢ an equilateral triangle has 3. ā¢ a circle has lots ā very many lines of symmetry.
Reflection
When you reflect a shape in a mirror line, you get its mirror image ā the same shape flipped over. If you fold a symmetrical shape along its line of symmetry, the two halves overlap exactly.
Worked examples
A line of symmetry on a square
- Fold the square so the top matches the bottom ā the halves match.
- You can also fold it side to side and along each diagonal.
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. The diagonals do not.
Answer: A rectangle has 2 lines of symmetry.
Reflecting a shape
- Draw a shape next to a mirror line.
- Sketch each point the same distance on the other side of the line.
Answer: You have drawn the reflection ā the mirror image.
A circle
- Fold a paper circle in half ā the halves match.
- You can fold it in half through the middle in many directions.
Answer: A circle has lots of lines of symmetry.
Where you see this in real life
- A butterfly's wings match on both sides of its body.
- Many letters, like A and T, have a line of symmetry.
- Folding paper in half to cut out a symmetrical shape.
- A face is roughly symmetrical down the middle.
Key words
- Symmetry
- When two halves of a shape are mirror images of each other.
- Line of symmetry
- A line that splits a shape into two equal mirror-image halves.
- Mirror line
- Another name for a line of symmetry.
- Vertical
- Going straight up and down.
- Horizontal
- Going straight across, from side to side.
- Reflection
- The mirror image of a shape in a mirror line.