Question

Determine whether each figure has rotational symmetry, line symmetry, both, or neither.

regular hexagon

parallelogram

kite

scalene triangle

Answer 1

- Regular hexagon: both. It has rotational symmetry of order 6 (rotations by 60°,120°, …,300°) and 6 lines of reflectional symmetry (through opposite vertices and through midpoints of opposite sides).

- Parallelogram (generic): rotational symmetry only. A generic parallelogram is symmetric under a 180° rotation (order 2) but has no reflection symmetry. (Special cases: a rectangle or a rhombus has additional reflection symmetry.)

- Kite (generic): line symmetry only. A (non‑rhombus) kite has one axis of reflection through a pair of opposite vertices but no nontrivial rotational symmetry. (A rhombus is a special case with more symmetry.)

- Scalene triangle: neither. No reflection axes and no nontrivial rotational symmetry.