Question

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

Answer 1

Equilateral triangle.

Further explanation

We at present know an equilateral triangle occupies three sides and angles that are congruent with three interior angles of each 60°.

Next, we discuss the order of rotational symmetry on an equilateral triangle.

• A figure possesses rotational symmetry if it can be rotated at an angle between 0° and 360° around a center point so that the figure coincides with the initial position again. It means the shape does not appear to change.
• The center of rotation is the point at which we rotate the figure, or, the center of the shape.
• The rotation angle is the angle we need to rotate, or in other words, the smallest angle at which shape can be rotated to coincide with itself.
• The order of rotational symmetry represents the number of times a shape fits on top of itself in one rotation.

See the attached picture.

• An equilateral triangle possesses rotational symmetry of order 3.
• The rotation angle of 120° is calculated from  $\boxed{ \ \frac{360^0}{3} = 120^0 \ }.$
• It can be rotated through 120° as much as 3 times still be the same original shape.  

When we rotate this shape, we discover three different positions, each of which looks the same.

Learn more

1. The order of rotational symmetry of rhombus brainly.com/question/4228574
2. A triangle is rotated 90° about the origin brainly.com/question/2992432
3. Determine the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: the equilateral triangle, rotational symmetry, order 3, three sides and angles, congruent, interior angles, the center of rotation, shape

Answer 2

Answer:- Equilateral triangle has an order 3 rotational symmetry.

Explanation:-

In geometry, a figure has rotational symmetry if it moves onto itself under rotation about an angle at center of rotation.

The order of rotational symmetry is the number of times the shape moves onto itself throughout a rotation of 360°.

An equilateral triangle has all its sides equal with equal interior angle of 60°.

It moves onto itself three times throughout a rotation of 360°.

⇒Equilateral triangle has an order 3 rotational symmetry.