Chapter 14.8, Problem 6CE

To determine

To describe all the rotational symmetries of the figure.

Answer to Problem 6CE

The figure equilateral triangle has 3 rotational symmetry.

Explanation of Solution

Given information:

The figure of an equilateral triangle.

The figure of equilateral triangle has the three rotational symmetry. Each symmetry has center O and rotates the figure onto itself. Note that $120°$ rotational symmetry is another name for point symmetry.

  $\begin{array}{l}\left(1\right)120°{\text{ rotational symmetry: R}}_{0,120}\\ \left(2\right)240°{\text{ rotational symmetry: R}}_{0,240}\\ \left(3\right)360°\text{ rotational symmetry: I is the identity}\text{.}\end{array}$

The identity mapping always maps a figure onto itself, we usually include the identity when listing the symmetries of a figure.

Therefore, the figure equilateral triangle has 3 rotational symmetry.