Question

which of the following transformations carry this regular polygon onto itself? image of a regular triangle with a horizontal line l and four options: rotation of 120° clockwise, reflection across l, rotation of 40° clockwise, rotation of 120° counterclockwise, all with checkmarks

Explanation:

Step1: Identify polygon type

The figure is a regular triangle (3 sides).

Step2: Check rotation symmetry

Regular n-gon has rotational symmetry every $\frac{360^\circ}{n}$. For n=3, $\frac{360^\circ}{3}=120^\circ$. So 120° clockwise/counterclockwise rotations map it to itself; 40° does not.

Step3: Check reflection symmetry

Line l is a line of symmetry (bisects two sides), so reflection across l maps it to itself.

Answer:

rotation of 120° clockwise, reflection across l, rotation of 120° counterclockwise