Question Video: Determining the Order of Rotational Symmetry of Regular Polygons | Nagwa Question Video: Determining the Order of Rotational Symmetry of Regular Polygons | Nagwa

# Question Video: Determining the Order of Rotational Symmetry of Regular Polygons Mathematics

The following figure is an equilateral triangle. Determine the order of rotational symmetry of the figure.

02:45

### Video Transcript

The following figure is an equilateral triangle. Determine the order of rotational symmetry of the figure. Option (A) order two, option (B) order three, option (C) order four, option (D) order six, option (E) the figure does not have rotational symmetry.

Let’s start by recalling that the order of rotational symmetry of a geometric figure is the number of times you can rotate the figure so it still looks the same as the original figure. And that’s over a rotation of 360 degrees. So let’s start by highlighting one of the vertices on this triangle. And then we consider we turn or rotate this triangle.

Because this is an equilateral triangle, if we rotated this about the center, then after 120 degrees, the highlighted vertex would now be at the base. The image after this rotation would look the same as the original figure. If we then rotated the image another 120 degrees or considered it as the original shape rotated 240 degrees, then the highlighted vertex would now be on the bottom left. So the image looks like the original shape. After a further 120 degrees of the last image or a complete 360-degree rotation, then the shape would be back to the original starting point.

To find the order of rotation, we need to count how many times in this 360-degree rotation the image looked the same as the original shape. So the image looked like itself once after a 120-degree rotation, twice after 240 degrees, and finally a third time when it was back in the original position. So we can give the answer that the order of rotational symmetry is order three.

But before we finish with this question, there’s a few things to note. The only reason that this triangle has an order of rotational symmetry of three is because it was an equilateral triangle. If we imagine we had even an isosceles triangle and we rotated it through 360 degrees to see how many times it looked the same as the original figure, we would find that that only happened once. And that’s when it’s in the original starting position. In this case, we would say that this isosceles triangle would have on order of rotational symmetry of order one.

Notice that that’s also what we mean when we say that the figure doesn’t have rotational symmetry, like we had in option (E). However, we can give our answer here as option (B) that this equilateral triangle and any equilateral triangle will have an order of rotational symmetry of order three.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions