Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Geometry
Similarity
What is Similarity?
Two figures are similar when their corresponding angles are equal and their corresponding sides are all in the same ratio. That common ratio is the length scale factor k. Areas and surface areas of similar figures are in the ratio k squared, and volumes are in the ratio k cubed, so a length ratio is recovered from an area ratio by taking a square root and from a volume ratio by taking a cube root.
This definition is part of the Geometry chapter in Cambridge O Level Mathematics (Syllabus D).
Similarity in context
Geometry marks are awarded for named reasons, not for plausible-looking numbers: every angle, length or similarity conclusion in this chapter must come from a property you can state in words, such as “angles on a straight line sum to 180°” or “the tangent–radius angle is 90°”. A diagram is evidence only where it is marked or given, never where it merely looks a certain way, because Cambridge exam diagrams are not drawn to scale.
Geometry marks are awarded for named reasons, not for plausible-looking numbers. Every angle, length or similarity conclusion in this chapter comes from a property you can name in words — and a diagram is evidence only where it is marked, never where it merely looks a certain way.
Common mistakes with Similarity
- “The areas are in the ratio \(49:81\), so the lengths are too.” Fix Take the square root: lengths are \(7:9\). For volumes, take the cube root. Going the wrong way through \(k^2\) and \(k^3\) is the most common similarity error there is.