Understanding Propositions 3.6: Rays and Common Points

Definition and Properties of Rays.A ray is a part of a line that starts at a specific point, called the endpoint, and extends infinitely in one direction.Unlike a line segment, which has two endpoints, a ray has only one endpoint and continues forever in one direction.Rays are denoted using an arrow symbol above two points, such as AB with an arrow on top, where A is the endpoint and B is any other point on the ray.Let's discuss the important properties of rays.Property one: A ray has exactly one endpoint. This point is where the ray begins.Property two: A ray extends infinitely in one direction. The ray continues forever without ending.Now let's look at how rays can share endpoints.Property three: Two different rays can share the same endpoint. Multiple rays can originate from the same point but extend in different directions.Let's move on to our final property.Property four: A ray is a subset of a line. Every ray lies on a line that extends infinitely in both directions.To summarize, a ray starts at a specific point called the endpoint and extends infinitely in one direction. It is denoted with an arrow above two points.