Symmetry
Understanding Symmetry
- Symmetry refers to an object being the same on both sides - a mirror image.
- It is an inherent characteristic in several geometric figures and patterns.
- A shape is said to possess symmetry if there are one or more lines where the shape can be folded along and the two halves correspond exactly in size and shape - this is known as a line of symmetry.
Types of Symmetry
- Reflective Symmetry: Reflective symmetry, also known as line or mirror symmetry, exists when an object can be folded in half and the two halves match exactly.
- Rotational Symmetry: Rotational symmetry exists when an object can be rotated around a central point and it still appears the same. The number of positions the object appears exactly the same in a full 360 degree rotation is known as the order of rotational symmetry. For example, a square has rotational symmetry of order 4, because it can be turned to appear the same 4 times within a full rotation.
- Translational Symmetry: Translational symmetry exists when an object can be moved (or “translated”) and it still appears the same. This is typical in repeating patterns.
Properties of Symmetry
- When a shape possesses symmetry, determining properties of the shape can often become simpler.
- For instance, in an isosceles triangle (a triangle with two sides of equal length), the base angles are always equal due to the line of symmetry cutting through the apex and base.
- In a similar way, the diagonals of any rectangle or square cut each other in half and at right angles due to their lines of symmetry.
Symmetry in the Coordinate Plane
- Symmetry can also occur in graphs and diagrams.
- Symmetry about the y-axis: If you can fold the graph along the y-axis and the two halves match exactly, then the graph is symmetrical to the y-axis.
- Symmetry about the x-axis: The same rule applies for symmetry about the x-axis. If you can fold the graph along the x-axis and the two halves match, then the graph is symmetrical to the x-axis.
- Symmetry about the origin: A graph is symmetrical about the origin if it appears the same when rotated 180 degrees around the origin.
Maintain these pointers about symmetry in mind. It’s a principle that emerges frequently in geometric and algebraic applications, making it a key part of geometry and measurement revision. Remember to practise identifying and working with different types of symmetry to build your familiarity and confidence.