Edexcel Mathematics (4XMAF) -Unit 2 - 4.3 Symmetry- Study Notes- New Syllabus
Edexcel Mathematics (4XMAF) -Unit 2 – 4.3 Symmetry- Study Notes- New syllabus
Edexcel Mathematics (4XMAF) -Unit 2 – 4.3 Symmetry- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A identify any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure
Example: name a quadrilateral with no lines of symmetry and rotational symmetry of order 2
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Lines of Symmetry and Rotational Symmetry
Line of Symmetry
A line of symmetry divides a shape into two identical mirror-image halves.
If you fold the shape along this line, both sides match exactly.
Rotational Symmetry
A shape has rotational symmetry if it looks the same after being rotated about its centre.
The order is how many times the shape matches its original position in one full turn \( (360^\circ) \).
- Order 1 → only matches after full turn
- Order 2 → matches twice in a full turn
- Order 4 → matches four times, etc.
Common Examples
Square → 4 lines of symmetry, rotational order 4
Rectangle → 2 lines of symmetry, rotational order 2
Equilateral triangle → 3 lines of symmetry, rotational order 3
Required Example
A quadrilateral with no lines of symmetry and rotational symmetry of order 2 is a:
Parallelogram
It matches after a \( 180^\circ \) rotation but has no mirror line.
Example 1:
How many lines of symmetry does a square have?
▶️ Answer/Explanation
Two diagonals and two through midpoints of opposite sides.
Conclusion: 4 lines of symmetry.
Example 2:
Find the order of rotational symmetry of a rectangle.
▶️ Answer/Explanation
A rectangle matches after \( 180^\circ \) and \( 360^\circ \).
Conclusion: Order 2.
Example 3:
Does a scalene triangle have a line of symmetry?
▶️ Answer/Explanation
All sides are different, so no mirror line exists.
Conclusion: No lines of symmetry.