Solved Examples on Rotational Symmetry
Example 1: Calculate the order of rotational symmetry for a regular hexagon?
Solution:
A regular hexagon, with its 6 equal sides, demonstrates rotational symmetry. It aligns perfectly after successive rotations of 60 degrees, completing a full 360-degree rotation.
Therefore, the order of rotational symmetry for a regular hexagon is 6.
Example 2: Find the angle of rotational symmetry for an equilateral triangle?
Solution:
An equilateral triangle, having 3 equal sides, exhibits rotational symmetry. It aligns perfectly after a 120-degree rotation around its center.
Hence, the angle of rotational symmetry for an equilateral triangle is 120 degrees.
Example 3: Determine the order of rotational symmetry for a square?
Solution:
A square, featuring 4 equal sides, can be rotated by 90 degrees successively four times around its center, completing a 360-degree rotation and aligning with its original position.
Therefore, the order of rotational symmetry for a square is 4.
Example 4: Calculate the angle of rotational symmetry for a regular pentagon?
Solution:
A regular pentagon, with 5 equal sides, demonstrates rotational symmetry. It aligns perfectly after a 72-degree rotation around its center. Hence, the angle of rotational symmetry for a regular pentagon is 72 degrees.
Rotational Symmetry
Rotational Symmetry of various geometric shapes tells how many times a shape aligns to its original position when it is rotated 360 degrees. Various figures having rotational symmetry are Square, Circle, Rectangle, Equilateral Triangle, and others.
Symmetry refers to the balanced likeness and proportion between two halves of an object, where one side mirrors the other. Conversely, asymmetry denotes a lack of this balance. Symmetry manifests in nature, architecture, and art, and can be observed through flipping, sliding, or rotating objects. Different types of symmetry include :
- Reflection
- Translational
- Rotational
Table of Content
- Rotational Symmetry Definition
- Examples of Rotational Symmetry
- Rotational Symmetry of a Parallelogram
- Rotational Symmetry of a Rectangle
- Rotational Symmetry of a Square
- Order of Rotational Symmetry of Square
- Rotational Symmetry of a Rhombus
- Rotational Symmetry of a Pentagon
- Rotational Symmetry of a Hexagon
- Rotational Symmetry of an Equilateral Triangle
- Triangle Rotational Symmetry
- Center of Rotation
- Angle of Rotational Symmetry
- Order of Rotational Symmetry
- Rotational Symmetry Letters
- Solved Examples on Rotational Symmetry
- Practice Problems on Rotational Symmetry