What Is Symmetry, in Geometry?

Shapes with symmetry can be rotated or reflected and stay identical

Shapes can have rotational or reflectional symmetry. Shapes with reflectional symmetry can be reflected over a line of symmetry and still look identical. Shapes with rotational symmetry can be rotated around a point and, at certain angles of rotation, still look identical.

Squares have many lines of symmetry, and have rotational symmetry (try rotating around their center point at multiples of $90^\circ$).

In the image below, the gray lines are the lines of symmetry for shape ABCD. Shape KLMN is congruent with shape ABCD, but rotated $90^\circ$ clockwise around the center point.