Symmetry
Line (reflective) symmetry
A shape has a line of symmetry if you could fold it along
that line and the two halves would land exactly on top of each other. The
fold line acts like a mirror: everything on one side is reflected onto a perfect match on the
other.
Some shapes have several such lines. A square has
4 lines of symmetry (two through opposite edges, two along the
diagonals), a rectangle has just 2, and an
equilateral triangle
has 3. In general a
regular
n-gon has exactly n lines of symmetry.
Rotational symmetry
A shape has rotational symmetry if you can
turn it about its centre by less
than a full turn and it looks exactly the same. The
order m counts how many times the shape matches
itself during one complete 360^\circ turn.
A square has rotational symmetry of order
4 — it looks the same after every
90^\circ — and an equilateral triangle has
order 3, matching after every
120^\circ. A regular n-gon has
rotational symmetry of order n.
Two ways a shape can match itself:
-
line symmetry — a fold line that maps the shape exactly onto itself;
-
rotational order — how many times the shape matches itself in one full
360^\circ turn;
-
a regular n-gon has
n lines of symmetry and rotational symmetry of
order n.
See the symmetry
Step through the figure: first a square with its four mirror lines, then an equilateral
triangle with its three, and finally the rotational order of each.