Symmetry
Line symmetry
- A shape has line symmetry if a mirror line splits it into two matching halves.
- A square has 4 lines of symmetry; a rectangle has 2; an equilateral triangle has 3.
Practice
How many lines of symmetry does a square have?
Two diagonals and two through the side midpoints: 4 lines.
Practice
Line symmetry means a mirror line splits the shape into:
A line of symmetry reflects one half exactly onto the other.
Rotational symmetry
- A shape has rotational symmetry if it fits onto itself as you turn it.
- The order is how many times it fits in one full turn. A square has order $4$.
- (Extended, solids) A plane of symmetry slices a solid into mirror halves; an axis of symmetry is a line you can spin it around.
Practice
What is the order of rotational symmetry of a square?
A square fits onto itself 4 times in one full turn.
You've got it
Key idea
- line symmetry: a mirror line gives two matching halves
- rotational symmetry order = times it fits itself in one full turn
- a square has 4 lines of symmetry and rotational symmetry of order 4