A ray line is a portion of a line. It can be defined as a line segment which is extended indefinitely in one direction. It is bounded by a point on one side and is not bounded the other side. This point is called the end point (sometimes referred as beginning point too). The other side which has no bounds extends to infinity in one direction.Ray Line

A ray is always a part of a line having one endpoint and a set of all points on only one side of the endpoint. In general, a ray is named by using two letters. The first letter must be the beginning point (endpoint) and the second letter being any point on the ray. An arrow with an endpoint over the letters is indicated to represent a ray. The above ray can be represented as $\overrightarrow{AB}$ where A is the endpoint and B is any point on the ray.
A light from a flash light is a real life example for a ray. The origin of the light which is the torch becomes the end point and one cannot measure exactly the distance the light travels in the direction pointed to. Sun rays are the best examples for rays starting from the end point Sun and goes in different directions and infinite distances.

Ray line segments can also be defined using betweenness of points like segments. A ray line segment is a part of a ray that is bounded by two points. The points are called the end points of the ray line segment.

Ray Line Segment

Consider a ray. Let A and B be two points on the ray. Then, the ray line segment between A and B, denoted by $\overline{AB}$, contains the end points A and B, every point on the line between A and B. A ray line segment AB is a locus of all points between the points A and B inclusive on the ray containing A and B.

Since a ray can be extended indefinitely on one side, its length can’t be determined. But, a ray line segment has end points and hence a ray line segment has length. The length of a ray line segment can be drawn using a straight edge with marked units of measurement. The length of the ray line segment is denoted by $\overline{CD}$.
Length of a Ray Line Segment

In the given figure, we have $\overline{CD}$ = 6 cm. However, measuring the length of the ray line segment with a straight edge is not accurate and is approximately equal. However, in the coordinates of the end points known, it is possible to measure the length of the ray line segment accurately by using the distance formula.
Consider two rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$. Both have common end point as A. So they can be represented in many ways. Few such ways are:

Opposite Rays

Now, consider the two rays going exactly in the opposite directions.

These two rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$ in the figure on the left form a single straight line through the common endpoint A. They are two rays but opposite in direction thus forming opposite rays.

Opposite Rays Example

Thus Opposite rays are two rays that are exactly opposite to each other in directions but have common endpoint.

Geometrically, we can also say, Opposite rays are formed by two collinear rays with a common endpoint, since the two rays form a line(lie on the same line). Thus we can also say that Opposite rays are coplanar.

Darth Maul's double light saber is a good real life example for opposite rays because the rays from the light saber are going 2 different directions.

Angle: When two rays have a common end point then they form a figure which is called as an angle. Such two rays are called the sides of the angle and their common point is called the vertex. The name of the angle is generally used from the name of the vertex. The letter that is used to name the vertex is used as the only letter when representing it as single letter name of as the middle of three letters which represent the two rays. The measure of these angles can be simply measured by using a protractor. Few examples of angles are given below :

Opposite Ray Example

Opposite rays form a straight angle which measure an angle of 180°.
Two or more ray line segments can intersect only when their rays lie in the same plane. When the ray line segments have same end points then they form an angle and the rays are called the sides of the angle. If the ray line segments do not have a common end points and if they lie on two parallel rays then they do not intersect. Also if the rays are not parallel, but their extended sides do not intersect at any length, then ray line segments do not intersect.

Ray Line Segment Intersection
Lines are rays look similar when represented on a piece of paper except for a small difference. A line has no end points on both sides where as a ray has end point on one side. If a line is divided into two parts then we get two rays. The point at which the line is cut becomes the common end point for both the rays. Thus we can say a ray is a part of a line.

Lines and Rays

$\overline{BC}$ is a line and $\overrightarrow{AB}, $\overrightarrow{AC}$ are rays.
A is the vertex of the rays and the point at which the line is cut.

Solved Examples

Question 1: Identify the ray lines in the following figure and indicate the common end point.

Lines and Rays Examples
$\overrightarrow{AB}$, $\overrightarrow{AC}$, $\overrightarrow{AD}$, $\overrightarrow{AE}$ are the ray lines and A is the common end point.

Question 2: In the above figure, in what other way can the ray line $\overrightarrow{AC}$ be represented as and why?
Ray line $\overrightarrow{AC}$ can be also represented as ray ray $\overrightarrow{AD}$ because C and D lie on the same ray.