What is symmetry? A geometric shape has symmetry if it can be folded, split, or turned in a way that makes it fit perfectly onto itself. It means the shape looks balanced and repeating.
Line Symmetry: A shape possesses line symmetry (or reflectional symmetry) if you can draw a straight line straight through it that splits it into two identical halves. If you fold the shape along this line, the two halves will overlap perfectly with no edges left hanging over. This folding line is called a line of symmetry. Think of a butterfly, a heart symbol, or the human face. Different shapes have different numbers of lines:
- A human hand has \(0\) lines of symmetry.
- A standard rectangle has exactly \(2\) lines of symmetry (running vertically and horizontally through the center).
- A regular square has \(4\) lines of symmetry (vertical, horizontal, and both diagonals).
Rotational Symmetry: A shape has rotational symmetry if it looks exactly the same more than once during a full \(360^\circ\) turn around its absolute center point.
- The order of rotational symmetry is the total number of times the shape looks identical to its starting position during one full circle turn.
- Every single shape on earth has an order of symmetry of at least \(1\) (because it will always look like itself once it returns back to the start).
- Think of a standard ceiling fan with \(3\) blades: turning it by \(120^\circ\) makes it look completely untouched, so it has a rotational symmetry of order \(3\).