Question

How does an equilateral triangle have rotational symmetry?

Answer 1

Hint: First, recall what an equilateral triangle is. Draw an equilateral triangle and check the changes when the triangle is rotated. Check for both clockwise and anticlockwise rotation. If the triangle looks exactly the same after rotation then we can say it has rotational symmetry.

Complete step-by-step answer:
We are asked how an equilateral triangle has rotational symmetry.

First let us know what an equilateral triangle is. An equilateral triangle has all its sides and angles equal.
A triangle has rotational symmetry if it looks the same after rotation of less than \[{360^{\text{o}}}\] .
Suppose \[ABC\] is an equilateral triangle.

As, triangle \[ABC\] is an equilateral triangle so,
  \[AB = BC = AC\] and \[\angle A = \angle B = \angle C\]
Now, if we rotate the triangle \[ABC\] by \[{120^{\text{o}}}\] clockwise we will get the triangle as,

We observe that after rotating, it looks exactly the same as before rotation since the sides and angles are equal.
Now, if we rotate the triangle \[ABC\] by \[{120^{\text{o}}}\] anticlockwise we will get the triangle as,

In this case too, we observe it looks exactly the same even after rotation.
Therefore, when we rotate an equilateral triangle by \[{120^{\text{o}}}\] clockwise or anticlockwise the triangle remains the same, that is there is rotational symmetry.
So, the correct answer is “ \[{120^{\text{o}}}\] ”.

Note: On the basis of sides, there are three types of triangles. These are equilateral triangle, isosceles triangle and scalene triangle. We have discussed equilateral triangle in the above question. Isosceles triangle is a type of triangle whose any two sides are equal and their corresponding angles are equal. Scalene triangle is a type of triangle whose all sides are unequal and all angles are unequal. Also, remember a scalene triangle does not have rotational symmetry.