Honors Geometry Companion Book, Volume 1

Example 1 Naming Points, Lines, and Planes The three fundamental geometric figures are points, lines, and planes. These three figures cannot be defined in terms of other figures, so they are referred to as undefined terms. 1.1.1 Understanding Points, Lines, and Planes (continued)

A point names a location and is represented by a dot. The dot must have some thickness or size when drawn, but an idealized point has no size because it is only a location. A point is named with a capital letter, such as P . A line is a straight path of points that extends infinitely in two opposite directions. An idealized line contains an infinite number of points and has length, but no thickness. A line is named with a lowercase letter or by drawing a double-headed arrow over the names of two points on that line. For example, the line here, which passes through the points X and Y , can be named  XY or  . A plane is a flat surface that extends infinitely. Points and lines are contained on a plane. A plane is named with a capital script letter, such as R , or with any three points on that plane, and these points are not on a single line. For example, ABC names a plane that contains points A , B , and C if A , B , and C are not contained on a single line. The points used for naming a plane can be listed in any order.

Points that lie on the same line are collinear points, and points that lie in the same plane are coplanar points. There are also terms to describe points that do not lie on the same line or plane: noncollinear and noncoplanar.

The given figure shows two planes, F and N ; five points, A , B , C , D , and E ; and two lines. Points B , C , D , and E are contained on F . So, B , C , D , and E are four coplanar points. Furthermore, N contains points A , B , C , and D , so these four points are also coplanar.


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