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

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

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

Answer: To determine which figure has an order 3 rotational symmetry, we need to understand what rotational symmetry is and what an order 3 rotational symmetry specifically means.

Rotational Symmetry: A figure has rotational symmetry if it can be rotated (less than a full circle) about its center and still look the same as it did before the rotation. The “order” of the rotational symmetry refers to the number of times the figure matches its original position during a full 360-degree rotation.

Order 3 Rotational Symmetry: A figure with order 3 rotational symmetry will look the same after a rotation of 120^\circ, 240^\circ, and 360^\circ. Essentially, it matches its original position three times during a full rotation.

Let’s analyze each figure:

  1. Right Triangle: A right triangle does not have rotational symmetry because rotating it by any angle less than 360^\circ will not make it look the same as its original position.

  2. Equilateral Triangle: An equilateral triangle has rotational symmetry of order 3. It looks the same after rotations of 120^\circ, 240^\circ, and 360^\circ.

  3. Regular Hexagon: A regular hexagon has rotational symmetry, but it is of order 6. It matches its original position after rotations of 60^\circ, 120^\circ, 180^\circ, 240^\circ, 300^\circ, and 360^\circ.

  4. Right Trapezoid: A right trapezoid does not have rotational symmetry because rotating it by any angle less than 360^\circ will not make it look the same as its original position.

Therefore, the figure that has an order 3 rotational symmetry is the equilateral triangle.