Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · 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 O Level Mathematics (Syllabus D).
Common mistakes with Symmetry
- “My reason was ‘circle theorem’.” Fix Name the property in full and identify the arc, chord or tangent it applies to. There are six angle theorems and three symmetry properties; saying which one is what makes the explanation complete.
- Quoting “a prism has 4 planes of symmetry” from memory 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.
Questions students ask about Symmetry
How do you know which circle theorem to name?
Identify the arc, chord, tangent or diameter marked in the diagram first, then match it to one of the six angle theorems or three symmetry properties — for example, “angles in the same segment are equal, both standing on chord AB.” Naming the fact in full is what earns the reasoning mark, not just the correct number.