Involving a line being parallel to itself

In summary, a student in math 11 honors is seeking help in finding information and opinions on the topic of whether or not a line can be parallel to itself for an essay assignment. The student has searched online but has had difficulty finding relevant sources. Despite receiving hints and guidance, the student is still struggling to come to a conclusion and is looking for a website that discusses the topic in depth. However, some members suggest that the question may not involve an opinion and instead the student should focus on appealing to the definition of parallel being used.
  • #1
KennyIsGod
3
0
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.
 
Physics news on Phys.org
  • #2
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
 
  • #3
Are you the same height as yourself? :-)
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
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:
 

1. How can a line be parallel to itself?

A line is parallel to itself when it is perfectly straight and at the same distance from itself at all points. This means that the line will never intersect with itself and will always maintain the same distance between all of its points.

2. Can any line be parallel to itself?

No, only a perfectly straight line can be parallel to itself. Curved or angled lines cannot be parallel to themselves because they will eventually intersect with themselves at some point.

3. What is the significance of a line being parallel to itself?

A line being parallel to itself is significant because it is used as a reference for determining the parallelism of other lines. It also helps in geometric constructions and calculations, such as finding the slope and equations of parallel lines.

4. How can you prove that a line is parallel to itself?

A line can be proven to be parallel to itself by showing that it has the same slope at all points along the line. This can be done by using the slope formula (change in y over change in x) and showing that the values are constant for all points on the line.

5. Are parallel lines the only lines that are parallel to themselves?

Yes, parallel lines are the only lines that are parallel to themselves. This is because the definition of parallelism requires two or more lines to never intersect, and a line can only intersect with itself if it is not straight.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
722
  • Feedback and Announcements
Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
5K
Replies
73
Views
3K
  • Introductory Physics Homework Help
Replies
30
Views
2K
  • Atomic and Condensed Matter
Replies
0
Views
155
  • Introductory Physics Homework Help
2
Replies
35
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Back
Top