Involving a line being parallel to itself...

[KennyIsGod]

My teacher for math 11 honors gave the class an essay to do the first day of school, and stated that we would need to write an essay, stating two sides of the opinion on whether or not a line is parallel to itself. I then have to convince the teacher why my opinion is right, logically. I've searched online for a while now and it's been difficult finding a website with opinions on this matter, so all I am basically asking is if anyone knows a site I can go to to find the information I seek. If I could also have your opinions on whether or not a line is parallel to itself, I would greatly apreciate it.

[PRodQuanta]

No. she said "line". That is singular, not plural. That means there is only one line. You need 2 lines to be parallel.

The word parallel is a comparison. You only have one line. How do you compare one line to nothing?

If it is an essay, I'm sure there is multiple answers. Give us some of your thoughts.

Paden Roder

[Tide]

Are you the same height as yourself? :-)

[jcsd]

http://mathworld.wolfram.com/ParallelLines.html

Look at the defitnion given above. Does a line intersect with itself?

I'm not sure there's a definite answer to this one, but you could certainly look on it as the degenerate case of parallel lines.

[KennyIsGod]

None of you know of a website which discusses this topic in depth, so I could base a lot of my essay on it? I'm pretty sure the main thing my teacher is looking for is logic on how I came to my conclusion that 1 line is or isn't parallel to itself. Thanks for the help so far though.

[Tide]

Actually, this particular problem had been discussed quite extensively on this site. You can do a search and find it - sorry, I don't recall exactly where it was.

I just wonder why you aren't willing to think it out for yourself after all the wonderful hints you've been given here. I recommend carefully considering the definition of parallel and discovering where the logic leads.

[KennyIsGod]

I would think it out for myself, but my teacher specifically stated that websites were needed which displayed the sides of this opinion. I've searched through googled, and just searched these message board and I have come up empty.

[Hurkyl]

The problem is there really isn't an opinion involved. As Tide suggested, you simply need to appeal to the definition of parallel you are using.


If the question is really "Which definition of parallel should we use?", then it needs a different approach. :smile: