A line of symmetry folds a figure onto itself. Rotational symmetry turns it onto itself, and the smallest turn that works is 360 degrees divided by the order.
How many lines of symmetry does a regular nonagon have? What is its smallest angle of rotational symmetry?9 lines; 40∘
How many lines of symmetry does a rectangle that is not a square have? What is its smallest angle of rotational symmetry?2 lines; 180∘
A regular polygon has rotational symmetry of order 10. How many sides does it have, and what is its smallest angle of rotation?10 sides; 36∘
How many lines of symmetry does a regular dodecagon have? What is its smallest angle of rotational symmetry?12 lines; 30∘
How many lines of symmetry does a parallelogram that is not a rectangle or rhombus have? What is its smallest angle of rotational symmetry?0 lines; 180∘
A regular polygon has rotational symmetry of order 12. How many sides does it have, and what is its smallest angle of rotation?12 sides; 30∘
How many lines of symmetry does a regular hexagon have? What is its smallest angle of rotational symmetry?6 lines; 60∘
How many lines of symmetry does an equilateral triangle have? What is its smallest angle of rotational symmetry?3 lines; 120∘
A figure matches itself when rotated 40 degrees. What is its order of rotational symmetry?9
How many lines of symmetry does a square have? What is its smallest angle of rotational symmetry?4 lines; 90∘
How many lines of symmetry does a kite that is not a rhombus have? What is its smallest angle of rotational symmetry?1 line; no rotational symmetry
A figure matches itself when rotated 72 degrees. What is its order of rotational symmetry?5
How many lines of symmetry does a regular decagon have? What is its smallest angle of rotational symmetry?10 lines; 36∘
How many lines of symmetry does a rhombus that is not a square have? What is its smallest angle of rotational symmetry?2 lines; 180∘
A figure matches itself when rotated 120 degrees. What is its order of rotational symmetry?3
How many lines of symmetry does a regular octagon have? What is its smallest angle of rotational symmetry?8 lines; 45∘
How many lines of symmetry does a circle have? What is its smallest angle of rotational symmetry?Infinitely many lines; any angle
A figure matches itself when rotated 60 degrees. What is its order of rotational symmetry?6
How many lines of symmetry does a regular pentagon have? What is its smallest angle of rotational symmetry?5 lines; 72∘
How many lines of symmetry does an isosceles triangle that is not equilateral have? What is its smallest angle of rotational symmetry?1 line; no rotational symmetry
How many lines of symmetry does a regular hexagon have? What is its smallest angle of rotational symmetry?
A regular polygon has one line of symmetry for each side.
It turns onto itself every 360 divided by 6 degrees.
The answer is 6 lines; 60∘.
Where students go wrong
Counting four lines of symmetry for a rectangle. Its diagonals are not lines of symmetry unless it is a square.
Also called line symmetry, rotational symmetry, reflectional symmetry or order of rotational symmetry.
What you can put on this worksheet
Regular polygons
How many lines of symmetry does a regular octagon have? What is its smallest angle of rotational symmetry?→ 8 lines; 45∘
Triangles, quadrilaterals and circles
How many lines of symmetry does an isosceles triangle that is not equilateral have? What is its smallest angle of rotational symmetry?→ 1 line; no rotational symmetry
Order of rotational symmetry
A regular polygon has rotational symmetry of order 10. How many sides does it have, and what is its smallest angle of rotation?→ 10 sides; 36∘
Questions about these worksheets
Yes. Every symmetry sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the symmetry questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: regular polygons, triangles, quadrilaterals and circles and order of rotational symmetry. Tick as many as you want and set how many of each, or let it spread them evenly.
Counting four lines of symmetry for a rectangle. Its diagonals are not lines of symmetry unless it is a square.