State whether or not each figure has rotational symmetry.
a) scalene triangle
b) equilateral triangle
c) rectangle
d) square
e) regular hexagon
a) A scalene triangle does not have rotational symmetry. Rotational symmetry requires that a figure can be rotated by some angle and still look the same. Since the sides of a scalene triangle are of different lengths, any rotation will change its appearance.
b) An equilateral triangle has rotational symmetry. It can be rotated by 120 degrees or multiples of 120 degrees, and it will still look the same.
c) A rectangle has rotational symmetry. It can be rotated by 180 degrees, and it will still look the same.
d) A square has rotational symmetry. It can be rotated by 90 degrees, 180 degrees, or 270 degrees, and it will still look the same.
e) A regular hexagon has rotational symmetry. It can be rotated by 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees, or 360 degrees, and it will still look the same.
To determine whether a figure has rotational symmetry, you need to find out if you can rotate the figure by a certain angle around a central point and it still appears the same. Let's analyze each figure to determine if it has rotational symmetry:
a) Scalene Triangle: A scalene triangle is a triangle with three unequal sides. It does not have rotational symmetry because if you rotate it by any angle, it will not look the same.
b) Equilateral Triangle: An equilateral triangle is a triangle with three equal sides. It has rotational symmetry. You can rotate it by 120 degrees (or multiples of 120 degrees) around its center, and it will appear the same.
c) Rectangle: A rectangle has rotational symmetry. You can rotate it by 180 degrees around its center, and it will look the same.
d) Square: A square has rotational symmetry. You can rotate it by 90 degrees (or multiples of 90 degrees) around its center, and it will appear the same.
e) Regular Hexagon: A regular hexagon is a polygon with six equal sides. It has rotational symmetry. You can rotate it by 60 degrees (or multiples of 60 degrees) around its center, and it will look the same.
In summary:
a) Scalene Triangle: No rotational symmetry.
b) Equilateral Triangle: Has rotational symmetry.
c) Rectangle: Has rotational symmetry.
d) Square: Has rotational symmetry.
e) Regular Hexagon: Has rotational symmetry.