In everyday language “definition” and “property” are often confused, but in geometry they have quite distinct meanings. The difference lies in the fact that a definition identifies the object uniquely, whereas a property does not.
Remark — Definition versus property
A property is a characteristic of a geometric object that does not identify it uniquely (other objects may share it). A definition is a description that corresponds exclusively to that object.
- “A square has 4 sides” property (rectangles also have 4 sides).
- “A square is a quadrilateral with the 4 sides and the 4 angles mutually congruent” definition.
- “A square is a rectangle with perpendicular diagonals” definition (two properties together uniquely identify the square).
Links
Topics: Euclidean geometry
Concepts: Definition · Property