Question

which figure has an order 3 rotational symmetry?
right triangle
equilateral triangle
regular hexagon
right trapezoid

Explanation:

• A right triangle: When rotated, it does not coincide with its original position 3 times in a \(360^{\circ}\) rotation.
• An equilateral triangle: When rotated by \(\frac{360^{\circ}}{3}=120^{\circ}\), it coincides with its original position. So, in a \(360^{\circ}\) rotation, it coincides 3 times.
• A regular hexagon: When rotated by \(\frac{360^{\circ}}{6} = 60^{\circ}\), it coincides with its original position. So, order of rotational symmetry is 6.
• A right trapezoid: When rotated, it does not coincide with its original position 3 times in a \(360^{\circ}\) rotation.

Answer:

equilateral triangle