Cambridge IGCSE Mathematics · Syllabus 0580 · Geometry
Symmetry
What is Symmetry?
A shape has symmetry when a reflection or a rotation leaves it looking exactly as it did before. In two dimensions a line of symmetry is a mirror line across which the shape maps onto itself, and the order of rotational symmetry is the number of times the shape matches itself during one full turn of 360 degrees. In three dimensions a plane of symmetry cuts a solid into mirror-image halves, and an axis of rotational symmetry is a line about which the solid can be turned onto itself.
This definition is part of the Geometry chapter in Cambridge IGCSE Mathematics.
Common mistakes with Symmetry
- “A prism has four planes of symmetry.” Extended E4.5 Fix Count from the cross-section you are given. An equilateral triangular prism has \(4\); a scalene one has \(1\). Three-dimensional symmetry is an Extended requirement; Core symmetry is counted in two dimensions only.
- Quoting “a prism has 4 planes of symmetry” from memory Extended E4.5 Fix Count from the given cross-section. An equilateral triangular prism has \(4\); a scalene one has \(1\).
Examiner tips on Symmetry
- The rhombus and the rectangle catch people out. A rhombus’s lines of symmetry are its two diagonals; a rectangle’s are the two lines through the midpoints of opposite sides. Neither shape has all four, and swapping them over is a common error. Only the square, which is both, has four.