If the union of 2 rays is a line, then the rays are opposite rays (T/F)
So I was answering this question: "If the union of 2 rays is a line, then the rays are opposite rays." Forgive my inexperience, while answering this question we have the ability to check with the answer sheet before the teacher checks off the assignment is done.
The answer provided by this sheet is "True", and I was wondering how this is possible, because my assumption that in the scenario in the image is no different than a line, while my teacher says overlap must be expressed. I do not wish to argue with my teacher, I simply am curious about the answer, he's a great guy and it's not like I lost points on it, and his explanation did not satisfy me. Here are the basic things both me and the teacher agree on (that I think is relevant).
1: A point is a exact location with 0 dimensions
2: A ray, and any section within a ray/line that is not itself a point has infinite points within it
However we differ in views on this:
3: The overlap between 2 rays, as long as it is not itself a point, is infinite, I believe that this infinity is the same as any other expressed here, and him thinking that this one is larger
A example he provided me, of which I do not quite understand its purpose in this conversation are 2 concentric circles with radii 1 and 2. He explains that the amount of ink used in the radius 1 circle is less than the radius 2 circle while both still having infinite points. But I *believe* this can easily be explained through different concepts not related to this. (If anything this probably supports my logic?)
One final thing I can deduce in my head that may side with my conclusion is this: that if you have one line on a number line every point (infinite) is located on that line. If you were to add another where the 2 lines completely overlap, I see no logical reason for additional points to be "covered" by the 2nd line.
If anyone could help explain to me how this works id be very grateful!
Edit: the definition used by me for "opposite rays" are two rays with the same starting point that run in opposite directions (180* flip)