Geometry - Lines, Line Segments, and Rays

Point: A point is a basic geometric element that represents a specific location in space. It is visually represented as a small dot and labeled with a capital letter, such as Point $A$. It has no length, width, or depth.

Line: A line is a collection of points extending infinitely in two opposite directions. Visually, a line is drawn with arrowheads at both ends to show it never stops. It is denoted as $\overleftrightarrow{AB}$ and has no fixed length.

Line Segment: A line segment is a finite portion of a line bounded by two distinct endpoints. Visually, it is shown as a straight path between two dots. It is denoted as $\overline{PQ}$ and has a measurable, definite length.

Ray: A ray is a part of a line that begins at a fixed starting point (endpoint) and extends infinitely in only one direction. Visually, it has a dot at the origin and an arrowhead at the other end. It is denoted as $\overrightarrow{XY}$, where $X$ is the starting point.

Intersecting Lines: When two or more lines cross each other at a single common point, they are called intersecting lines. The point where they meet is called the point of intersection. Visually, these lines look like the letter 'X'.

Parallel Lines: Parallel lines are lines in the same plane that never meet or intersect, regardless of how far they are extended. They always maintain the same distance from each other, looking like the rails of a railway track. This is written as $l \parallel m$.

Perpendicular Lines: Two lines that intersect at a right angle ($90^\circ$) are called perpendicular lines. Visually, they form a perfect 'L' or '+' shape. This relationship is represented by the symbol $\perp$, for example, $AB \perp CD$.

Collinear Points: Three or more points are said to be collinear if they all lie on the same straight line. If they do not lie on the same line, they are called non-collinear points.