Geometry
Symmetry
Count lines of symmetry, find the order of rotational symmetry, and work out the smallest turn that leaves a shape looking the same.
A shape has a line of symmetry if you can fold it along that line and the two halves land exactly on top of each other. Some shapes have none, some have one, and a regular shape has as many as it has sides.
Two different kinds of symmetry
Line symmetry is about folding. Rotational symmetry is about turning: the order of rotational symmetry is how many times a shape looks the same during one full turn. They do not always come together — the letter S has rotational symmetry of order 2 and no line of symmetry at all, and the letter A has one line of symmetry and no rotational symmetry.
Worked example
How many lines of symmetry does a rectangle that is not a square have?
Fold it left onto right. The two halves match, so that is one line.
The fold goes through the middles of the two long sides.
Try it together
Now let us describe the symmetry of a regular pentagon completely.
A regular pentagon has five equal sides and five equal angles. Three questions, and each one answers the next.
1.How many lines of symmetry does it have?
Have a go
Have a go on your own: how many lines of symmetry does a regular octagon have?
Hint: An octagon has eight sides.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.