Definition
Symmetry
A figure has symmetry when a stated transformation moves it so it matches itself exactly.
What it means
Symmetry means a change can be made without changing the figure's overall arrangement. You must say what change you are testing. A reflection tests line symmetry; a turn about a centre tests rotational symmetry.
Remember it
Change the position in a precise way; the figure still fits itself.
Example
A square has line symmetry because reflection in any of four symmetry lines maps it onto itself. It also has rotational symmetry because turns of 90°, 180°, and 270° about its centre make it match.
Watch for
A shape that only looks balanced is not necessarily symmetric; an exact stated transformation must map every part onto the figure.
Common mix-up
‘Symmetry’ names the broad idea. Line symmetry and rotational symmetry name different transformations.
Exact meaning
A figure has symmetry with respect to a transformation if applying a non-identity transformation of the stated type maps the figure onto itself. Common school examples are reflectional and rotational symmetry.