Symmetry: shapes and mirrors
📖 In short
Look at a butterfly: its right wing is the mirror image of its left wing. We say the butterfly is “symmetrical”, and the line down its middle is the “line of symmetry”. If we fold the shape along that line, the two halves match exactly.
🤩 Did you know?
- Every snowflake has 6 arms, and no two snowflakes are exactly alike.
- A square has 4 lines of symmetry, and a rectangle only 2.
- Some letters are symmetrical: the letters A, H, O, T and X are symmetrical.
- A human face is nearly symmetrical, but not quite: its two halves are slightly different.
🔎 Find out more
🌟 Line of symmetry
A line of symmetry splits a shape into two matching halves, as if one were the other's reflection in a mirror. It can be vertical, like a human face, or horizontal, like a mountain reflected in a lake.
🔍 How many lines?
A rectangle has two lines, a square 4 and an equilateral triangle 3. A circle has countless lines: every line through its center is a line of symmetry!
💡 Symmetry in nature
We find symmetry in animals' bodies, in tree leaves, in snowflakes with 6 matching arms, and in flowers whose petals repeat around the center.
🎯 Symmetry in art
Architects love symmetry because it gives a feeling of balance and beauty. Look at the fronts of mosques and palaces, and at traditional patterns and rugs: they're all symmetrical.
📊 See it in a picture
🧮 Worked examples
- Square: 4 linesOne vertical, one horizontal and two diagonals.
- Rectangle: 2 linesOnly one vertical and one horizontal; the diagonals aren't lines of symmetry.
- The number 8Symmetrical about a vertical line and a horizontal line.
📚 Key words
- Symmetry
- When the two halves of a shape are mirror images of each other
- Line of symmetry
- The line that splits a shape into two symmetrical halves
- Congruent
- Two shapes exactly the same in shape and size
🧪 Try it at home
Fold a sheet of paper in half, put drops of watercolor near the fold on one side, then close the paper, press it and open it. You'll find a symmetrical butterfly! Where is its line of symmetry?
🧩 Test yourself
1 How many lines of symmetry does a square have?
2 What happens if we fold a symmetrical shape along its line?
3 Which of these letters is symmetrical?