2D shape and pattern
Symmetry
Hold a mirror along a line through a shape. If what you see matches the half you covered, you have found a line of symmetry.
What a line of symmetry is
A LINE OF SYMMETRY splits a shape into two halves that mirror each other exactly. Fold along the line and the two halves would land exactly on top of each other. A shape with at least one such line is SYMMETRICAL.
The mirror test
Place a small mirror along the line you want to test, standing upright. Look at the reflection. Does it show exactly what is hidden behind the mirror? If yes, that is a line of symmetry. If no, it is not. Try three directions: VERTICAL (up and down), HORIZONTAL (across), and DIAGONAL (corner to corner).
Colour counts too
A pattern can be the right SHAPE on both sides and still not be symmetrical — because the colours do not match. When you test a coloured pattern, the reflection must match in shape AND colour. If one side is red where the other is blue, that line is not a line of symmetry, however neat the shape looks. A pattern can easily end up with 0 lines of symmetry for this reason.
How many lines do triangles have?
EQUILATERAL — 3 lines of symmetry, one through each corner. ISOSCELES — 1 line, through the corner between the two equal sides. SCALENE — 0 lines. Nothing matches, so nothing mirrors. Notice the pattern: the more equal sides, the more lines of symmetry.
Worked examples
Does this pattern have a vertical line of symmetry?
- Stand a mirror upright through the middle, top to bottom.
- Compare the reflection with the hidden half.
- The colours are different on the two sides.
Answer: No — it is not a line of symmetry
Lines of symmetry in an equilateral triangle
- Try a line from each corner to the middle of the opposite side.
- Each one gives two matching halves.
- There are three corners.
Answer: 3 lines of symmetry
Lines of symmetry in a scalene triangle
- All three sides are different lengths.
- So no fold can make the halves match.
Answer: 0 lines of symmetry
Testing all the directions
- Check vertical: no match.
- Check horizontal: no match.
- Check both diagonals: no match.
Answer: The pattern has 0 lines of symmetry
Where you see this in real life
- Butterflies have one line of symmetry down the middle of their body.
- Many national flags are symmetrical — but only if the colours match on both sides.
- Tile patterns in buildings often use symmetry so the design repeats neatly.
Key words
- Line of symmetry
- A line where a shape folds into two matching halves.
- Symmetrical
- Having at least one line of symmetry.
- Reflection
- The mirror image of a shape.
- Vertical
- Going straight up and down.
- Horizontal
- Going straight across.
- Diagonal
- Going from one corner towards another.