Square
4 lines; rotational order 4.
Learning Objectives
- identify line symmetry;
- identify rotational symmetry;
- state order of rotational symmetry;
- complete symmetric figures;
- recognise symmetry in regular polygons.
Introduction
This lesson develops Symmetry from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Line Symmetry
A line of symmetry divides a figure into two mirror-image halves.
Rotational Symmetry
A figure has rotational symmetry if it matches itself during a turn of less than 360ยฐ.
Order of rotational symmetry = number of matching positions in one full turn.
Common Examples
Rectangle
2 lines; rotational order 2.
Equilateral triangle
3 lines; rotational order 3.
Regular pentagon
5 lines; rotational order 5.
Try It: Rotational Symmetry
For a regular polygon, the order of rotational symmetry equals the number of sides.
๐ง Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- How many lines of symmetry does a square have?
- State the rotational order of a rectangle.
- How many lines of symmetry does a regular hexagon have?
- Does a scalene triangle have line symmetry?
- State the rotational order of a regular octagon.
โ Check Your Work
Show answers and working
- 4.
- 2.
- 6.
- No.
- 8.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Line symmetry creates mirror halves.
- Rotational order counts matching positions in 360ยฐ.