Key ideas
- A line of symmetry splits a shape into two halves that are mirror images. If you folded along it, the halves would match exactly.
- Some shapes have more than one line of symmetry, and some have none.
- Reflecting: each square ends up the same distance from the mirror line, on the other side.
- Count squares straight across to a vertical line, or straight up or down to a horizontal line.
- For a diagonal mirror line, count diagonally, corner to corner, at right angles to the line. Squares that touch the line stay where they are.
- Check your reflection by imagining folding the page along the mirror line.
the shape its reflection - - - the mirror line
Lines of symmetry
How many lines of symmetry does a rectangle have?(1 mark)
Try folding it.
In plain EnglishFold it in half from top to bottom: the halves match. Fold it from side to side: they match again.
What about the diagonals?A rectangle has 2 lines of symmetry✓1
In plain EnglishFolding along a diagonal does not work: the corners don't land on top of each other. So the diagonals are not lines of symmetry.
⚠ A common mistake: a rectangle's diagonals are not lines of symmetry. A square's are, because all its sides are equal.
Vertical mirror line
Reflect the shape in the vertical mirror line.(2 marks)
Count across to the line.
In plain EnglishTake one square at a time. The square marked 1 is 1 square from the mirror line. The square marked 3 is 3 squares away.
Same distance on the other side.Each square is the same distance from the line on the other side✓2
In plain EnglishCount the same number of squares across on the other side of the line, and shade. Rows don't change: each square stays at the same height.
Horizontal mirror line
Reflect the shape in the horizontal mirror line.(2 marks)
Count down to the line.
In plain EnglishNow count up and down. The square marked 1 is 1 square above the line. The square marked 3 is 3 squares above it.
Same distance below.Each square is the same distance below the line✓2
In plain EnglishCount the same number of squares below the line. Columns don't change: each square stays in the same column.
Diagonal mirror line
Reflect the shape in the diagonal mirror line.(2 marks)
Count diagonally to the line.
In plain EnglishWith a diagonal line, count corner to corner. The square marked 2 is 2 diagonal steps from the line. Imagine folding the grid along the line.
Same distance on the other side.Each square is the same number of diagonal steps away, on the other side✓2
In plain EnglishA square that is 2 along and 0 down ends up 0 along and 2 down. The rows and columns swap over.
Tip: turn the page so the mirror line is straight up and down. Then it is just like a vertical reflection.
Two mirror lines
Complete the pattern so that both dashed lines are lines of symmetry.(3 marks)
Reflect in the vertical line.
In plain EnglishFirst reflect the shape across the vertical line, as usual.
Then reflect everything in the horizontal line.The pattern now has 2 lines of symmetry✓3
In plain EnglishNow reflect the whole top half, both pieces, down across the horizontal line. The finished pattern is the same in all four quarters.
0 of 0 complete
Your turn
For the grids, tap the squares to shade the reflection, then press Check. Tap a square again to unshade it. Stuck? Tap Need a hint?