Rotational symmetry

Learning Objectives Define rotational symmetry, center of rotation, order of rotation, and angle of rotation. Identify whether a two-dimensional figure possesses rotational symmetry. Determine the center of rotation for a given geometric figure. Calculate the order of rotational symmetry for a figure. Calculate the smallest positive angle of rotational symmetry. Distinguish between rotational symmetry and reflectional (line) symmetry in complex shapes. Apply the properties of rotational symmetry to solve problems involving regular polygons. Have you ever noticed how a spinning fan blade, a Ferris wheel, or a car's hubcap looks the same at several points during one full turn? 🎡 That's rotational symmetry in action! In this tutorial, we will explore the geometric...

TermDefinitionExample Rotational SymmetryA property of a shape where it looks identical to its original position after being rotated by an angle less than 360° around a central point.A square looks the same after a 90°, 180°, and 270° rotation around its center. Center of RotationThe fixed point about which a figure is rotated. For many geometric shapes, this is their geometric center.For a circle, the center of rotation is the center of the circle. For a regular hexagon, it is the point where all its diagonals intersect. Order of Rotational SymmetryThe number of times a figure maps onto itself during a full 360° rotation. The order must be an integer greater than 1 for a shape to have rotational symmetry.An equilateral triangle has an order of 3 because it maps onto itself at 120°, 240°,...

Calculating the Angle of Rotation \text{Angle of Rotation} = \frac{360^\circ}{\text{Order of Rotation}} Use this formula when you know the order of rotational symmetry and need to find the smallest angle of rotation. The order is the number of times the shape fits into itself in a full turn. Calculating the Order of Rotation \text{Order of Rotation} = \frac{360^\circ}{\text{Angle of Rotation}} Use this formula when you know the smallest angle of rotation that maps a figure onto itself and you need to find the order. Symmetry of Regular Polygons For a regular polygon with n sides, the order of rotational symmetry is n. This is a shortcut for all regular polygons. The number of sides directly tells you the order of rotational symmetry. From this, you can easily calcula...