Symmetry

4 minQuiz at the end

Line (Reflection) Symmetry

A shape has line symmetry if it can be folded so that one half fits exactly on the other. The fold line is the line of symmetry (or mirror line).

ShapeLines of symmetry
Equilateral triangle3
Square4
Rectangle2
Regular hexagon6
CircleInfinite
Scalene triangle0

Rotational Symmetry

A shape has rotational symmetry if it looks identical after a rotation of less than 360Β°.

The order of rotational symmetry is how many times the shape looks the same in one full turn.

ShapeOrder
Square4
Equilateral triangle3
Rectangle2
Regular hexagon6
Scalene triangle1 (no rotational symmetry)

Order 1 means the shape only looks the same after a complete 360Β° turn β€” effectively no rotational symmetry.

Symmetry in Coordinates

If a shape is symmetric about the y-axis, for every point (x, y) there is a corresponding (-x, y).

Using Symmetry

Symmetry helps solve problems by reducing the number of angles or lengths you need to calculate β€” a property shared by symmetric parts.