What are the rotational symmetries of a square? How many lines of reflection symmetry does it have? What about a regular pentagon? A regular hexagon?
(Regular hexagon) A regular hexagon features 6 lines of reflection symmetry, passing through opposite vertices and midpoints of opposite sides. It has rotational symmetries of order 6, corresponding to rotations of 60°, 120°, 180°, 240°, 300°, and 360°.
(Regular pentagon) A regular pentagon has 5 lines of reflection symmetry, each passing through a vertex and the midpoint of the opposite side. Its rotational symmetries are of order 5, with rotations of 72°, 144°, 216°, 288°, and 360°.
(Square) A square possesses 4 lines of reflection symmetry, passing through opposite vertices and midpoints of opposite sides. It has rotational symmetries of order 4, corresponding to rotations of 90°, 180°, 270°, and 360° around its center.
Explanation
The question asks for the symmetries of regular polygons. While the provided context only details the symmetries of a circle (complete rotational symmetry and infinite lines of reflection symmetry via diameters), the properties of regular polygons dictate that a regular polygon with n sides has n lines of reflection symmetry and rotational symmetry of order n.
Solution Steps
Step 1: Identify the number of sides (n) for each shape: Square (n=4), Regular Pentagon (n=5), Regular Hexagon (n=6).
Step 2: Determine lines of reflection symmetry, which equals n for a regular polygon.
Step 3: Determine rotational symmetries, which are multiples of 360°/n, resulting in an order of n.