Symmetry and reflecting shapes
Maths · Key Stage 2 · The School
What a line of symmetry is
A shape has a line of symmetry if you can fold it exactly in half, and both halves match perfectly. A square folds neatly along its middle, so it has a line of symmetry there. Not every fold works. Only the ones where both halves match count. A shape can have one line of symmetry, several, or none at all. A scalene triangle has none, since no fold ever makes both sides match.
Some shapes have several
A square actually has four lines of symmetry: straight down the middle, straight across the middle, and along both diagonals. A regular hexagon has six. A circle has an endless number, since every line through its centre folds it in half. The more regular and even a shape is, the more lines of symmetry it tends to have. This link is worth noticing as you look at more shapes.
Reflecting a shape
Reflecting a shape flips it across a line, like a mirror. Every point moves to the opposite side, the same distance from the line as it started. A shape and its reflection always look identical, just flipped. Picture your own reflection in a mirror: it matches you exactly, just the wrong way round.
Reflecting a triangle across a line
A triangle sits with one point 3 squares from a vertical line. To reflect it, move that same point 3 squares on the OTHER side of the line. Do the same for every other point of the triangle. Join the new points up. The new triangle is the exact mirror image, the same distance from the line as the original, just flipped.