Over two thousand years ago, Euclid defined a line as a "breathless length that lies evenly within the points on itself." In more modern language, a line is straight, has no width and goes on forever. Euclid was especially interested in parallel lines -- lines that never meet. Early in the 17th century Rene Descartes re-imagined the Euclidean plane on a fixed background, with a horizontal x-axis and a vertical y-axis, on which we define lines by their "slope" -- their relation to the x-axis. In modern terms, parallel lines are lines that have the same slope.
When an apparent line does have an endpoint, it is no longer called a line. If there is only one endpoint it is a "ray," and if there are two endpoints it is a "line segment." A line segment has a specific length, whereas lines and rays do not. Most of the simple shapes in classical plane geometry, including triangles, squares and polygons, are composed of line segments. Circles and curves are not made up of lines, rays or line segments, but rather the interactions between lines and curved figures -- an important part of geometry in both ancient and modern times.
Lines that intersect geometric figures often have their own names. For example, a line that goes through a circle is called a "secant," and the part of the secant that is within the circle is called a "chord." Chords are also line segments, and any line segment drawn from the middle of any chord to the center of the circle is always perpendicular to the first chord. The longest chord that can be drawn in a circle is the diameter of that circle, and passes through the circle's center. In figures that have angles -- like triangles and squares -- a line segment drawn from a vertex that bisects the angle is called a "bisector" of the figure.
A line that touches a curved figure at one point is called a "tangent." If a line segment is drawn from the center of a circle to the point at which a tangent line touches the circle, the line and the line segment are perpendicular. A tangent line to the curve of a graphed function describes how the curve is changing at the tangent point. For example, at the point where a curve changes direction, the tangent line will be horizontal.