AMSCO'S Geometry. New York - Rye High School

Definitions, Lines, and Line Segments 71-3 DEFINITIONS, LINES, AND LINE SEGMENTSQualities of a Good DefinitionA definition is a statement of the meaning of a term.When we state a definition,we will use only undefined terms or terms that we have previously defined.The definition of a term will state the set to which the term belongs and thequalities that makes it different from others in the set.Collinear PointsDEFINITIONA collinear set of points is a set of points all of which lie on the same straight line.This definition has the properties of a good definition:1. It is expressed in undefined words.Set, point, and line are undefined words.2. It states the set to which the defined term belongs.The set is a set of points.3. It distinguishes the term from other members of the class.The points must be on the same straight line.EA, B, and C are collinear points.D, E, and F are noncollinear points.A B CDEFINITIONA noncollinear set of points is a set of three or more points that do not all lieon the same straight line.DFThe Distance Between Two PointsEvery point on a line corresponds to a A B C D E F G Hreal number called its coordinate. Tofind the distance between any two 1 0 1 2 3 4 5 6points, we find the absolute value of thedifference between the coordinates ofthe two points. For example, the distance between G and C, written as GC, is5 1 4. We use absolute value so that the distance between any two pointsis independent of the order that we subtract the coordinates.