Question

1. determine the rotational and reflectional symmetry for the shapes below. a. m b. regular heptagon c.

Explanation:

Step1: Analyze letter M

The letter M has no rotational symmetry as it does not look the same after any non - full rotation. It has 1 vertical line of symmetry.

Step2: Analyze regular heptagon

A regular heptagon has 7 rotational symmetries corresponding to rotations about its center by angles $\frac{360^{\circ}}{7}, \frac{2\times360^{\circ}}{7},\cdots,\frac{6\times360^{\circ}}{7}$. It also has 7 lines of symmetry, each passing through a vertex and the mid - point of the opposite side.

Step3: Analyze sun - like shape

The shape has 8 equal parts. It has 8 rotational symmetries corresponding to rotations about its center by angles $\frac{360^{\circ}}{8}, \frac{2\times360^{\circ}}{8},\cdots,\frac{7\times360^{\circ}}{8}$. It has 8 lines of symmetry, some passing through opposite vertices and some passing through the mid - points of opposite "petals".

Answer:

A. Rotational symmetry: None; Reflectional symmetry: 1 line of symmetry.
B. Rotational symmetry: 7 - fold (rotations by $\frac{360^{\circ}}{7}, \frac{2\times360^{\circ}}{7},\cdots$); Reflectional symmetry: 7 lines of symmetry.
C. Rotational symmetry: 8 - fold (rotations by $\frac{360^{\circ}}{8}, \frac{2\times360^{\circ}}{8},\cdots$); Reflectional symmetry: 8 lines of symmetry.