Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Symmetries of a polygon
Describe rotations and reflections preserving a polygon
Problem types
- Decide which figure has rotational symmetry
- Count and describe polygon symmetries
- Regular polygon that maps onto itself under given rotations
Builds on
- Translations, reflections, and rotations
- Parallel lines, perpendicular lines, and symmetry · Earlier idea
A line of symmetry is a reflection that maps a polygon onto itself, so counting lines of symmetry counts some of its symmetries.
Leads to
- Constructing the image of a figure · Extend the idea
A symmetry is a rotation or reflection that maps a figure onto itself. Mapping a figure onto a different position uses compositions of the same transformations.
- The complex plane · See it applied
The n-th roots of unity are the vertices of a regular n-gon, whose rotations are multiplications by those roots.
Related skills
- Odd, even, and periodic trig functions · Related idea
The symmetries of a regular polygon and of the unit circle explain why sine and cosine values repeat and reflect.
- Classifying quadrilaterals · Related idea
Which quadrilateral a shape is determines its lines and rotations of symmetry, such as the four lines of a square.
- Congruence criteria for triangles · Shared foundations
- Dilations and similarity · Shared foundations
- What slides, flips, and turns keep the same · Shared foundations
Open the interactive map to explore lessons and skill connections.