Defining and Constructing Objects

A point is a geometric object that cannot be constructed using simpler objects. Meaning, it is an undefined term, as opposed to a defined term. Instead, it has to be described using its characteristics. One possible description is that a point is an object with no size, indicating a location in space. It is represented graphically with a dot.

A line, just like a point, is an undefined term. It is a one-dimensional object of infinite length with no width or height that never bends or turns. Its graphical representation is a straight line with arrowheads on either end, indicating that it continues indefinitely in both directions.

For each pair of non-identical points, it is possible to draw exactly one unique line through them. Thus, a line can be named using any two of the infinitely many points that lie on it. The above line could be named $\overleftrightarrow{AB},$ $\overleftrightarrow{BA},$ or line $\ell.$ A set of two or more points that lie on the same line is said to be collinear.

The line segment $\overline{AB},$ or segment $\overline{AB}$, consists of the endpoints $A$ and $B,$ and every point on line $\overleftrightarrow{AB}$ located between $A$ and $B.$ Notice that, a segment, unlike a line, does not extend infinitely — it is bound by its endpoints.

Between two non-identical points, it's possible to draw exactly one unique segment.

A plane is similar in its definition to a line, though it is two-dimensional. That is, it has an infinite width and length, but no height. It is represented by what could be seen as a floor or a wall, extending without end.

Through any three points not on the same line, exactly one plane can be drawn. This plane can be named using these points, as plane $ABC,$ or alternatively as plane $P.$ A set of points that are contained by the same plane are said to be coplanar.

A ray is a portion of a line, starting at an endpoint and extending indefinitely. The notation for a ray starts with the endpoint and another point on the ray, with an arrow drawn above it. For example, the ray below would be represented by: $\overrightarrow{AB}.$

The ray $\overrightarrow{AB}$ lies on the line $\overleftrightarrow{AB},$ starting at $A,$ continuing through $B,$ and then continuing indefinitely in that direction. Note that it's important to distinguish between the ray $\overrightarrow{AB}$ and $\overrightarrow{BA};$ although they both lie on the same line, they point in opposite directions and have different endpoints.