What You'll Learn
✓ How shapes repeat themselves through rotational and reflectional symmetry
✓ The properties and names of all common 2D and 3D shapes
✓ How to identify planes of symmetry in 3D objects
✓ Converting between length, mass, capacity, and area/volume units
✓ Understanding nets and how 3D shapes unfold
✓ Circle terminology and key measurements
Rotational Symmetry
The Big Idea: Rotational symmetry measures how many times a shape looks identical as you spin it around its centre.
What Is Rotational Symmetry?
When you rotate a shape 360° around its centre, you might see it match its original position multiple times. The order of rotational symmetry is the number of times the shape looks identical during a complete rotation.
Example: A square looks identical 4 times as you rotate it 360°, so it has rotational symmetry order 4.
How to Find Rotational Symmetry
- Use tracing paper: Trace the shape and draw an arrow pointing upwards
- Rotate 360°: Slowly turn the tracing paper and count how many times the shape matches the original
- Count includes the start: Returning to the original position counts as 1
- Remember: Every shape has at least order 1 (it matches when fully rotated)
⚠️ Common Mistake: Order 1 means "no rotational symmetry" in everyday language, but mathematically, all shapes have order 1 minimum.
Q1: A rectangle has rotational symmetry. What is its order?
Q2: An equilateral triangle has what order of rotational symmetry?
💡 Exam Tip
When asked to shade squares to create rotational symmetry, think about the rotational centre and imagine the shape rotating around it. Use the tracing paper technique to check your answer.
Lines of Symmetry
The Big Idea: A line of symmetry (or mirror line) divides a shape so that one half is a reflection of the other.
Understanding Reflection Symmetry
If you fold a shape along a line of symmetry, both halves sit exactly on top of each other. The two halves are identical mirror images.
Visual Test: Fold paper along the line—if both halves match perfectly, it's a line of symmetry.
Lines of Symmetry in Common Shapes
- Equilateral triangle: 3 lines (through each vertex and opposite side)
- Isosceles triangle: 1 line (through the vertex angle)
- Square: 4 lines (2 through opposite sides, 2 through opposite corners)
- Rectangle: 2 lines (through opposite sides only, NOT diagonals)
- Circle: Infinite lines (any line through the centre)
- Regular pentagon: 5 lines
⚠️ Important: A rectangle's diagonals do NOT create lines of symmetry. If you fold along a diagonal, the two halves don't sit on top of each other exactly.
Completing Shapes Given a Line of Symmetry