Is a line parallel to itself? Explain.?

Question

If M is parallel to N, is N parallel to M? Explain.
If M is parallel to N and N is parallel to P is M parallel to P? Explain.

Answer 1

No, a line isn't "parallel to itself". "Parallel" is a binary comparison, meaning you need two things to compare. There's another problem with misusing the term like this: if you say parallel lines have the same slope when graphed on a 2D plane, then the answer would be yes, but if you say parallel lines on a plane are lines that have no points in common, the answer would be no.

If M is parallel to N, then yes, N is parallel to M. That goes with the definiton. Either two lines are parallel lines or they're not.

As for the last statement, yes, the transitive property holds for paralell lines. It seems intuitive, though the proof for lines in 3D space (where parallel lines are defined as not only never meeting, but having a constant for the distance between any pairs of points closest to each other) is a little harder than it seems.

Answer 2

The first axiom is true as if you began with either line N or M as a body of reference, every point on the other would be seen to keep the dame distance from any corrresponding point on the line you chose to refer to, that is you would observe the lines to be parallel. If you and another observer were to carry out this experiment simultaneously, with the other observer beginning with the other line, he would record the same observations as you, i.e he would also visualize the two lines to be parallel.

The second axiom is also true. We have just proved that the parallel nature of lines is independent of the observer, so we have proved that N is parallel to M, and M is parallel to N, whatever the conditions. Now if we introduce a 3rd line P which is parallel to N and which we mean to prove to be also parallel to M, we would consider P to be an extension of N (as they are parallel, and if joined create a straight line, parellel to both) and then repeat our thought experiment with two observers, and our results would show that our proof holds true for M and this line too. Now if we subtract from this line the length of N, we are left with M and P, which are parallel to each other.

Answer 3

A line is not necessarily linear. All curves are lines. Even a best defined straight line can be expressed as a curve. So a line is not parallel to itself!

Unless both M and N are in a plane, a pair of mutually parallel lines will not exist though each of these is "theoretically nearest to straight line"!

Unless both M and P are lying on two mutually perpendicular planes and when both said perpendicular planes intersects as line M , lines M and P cannot be parallel (though all three lines M, N and P are "theoretically nearest to straight lines")!

Answer 4

If M is parallel to N, N is indeed parallel to M. Distance between M and N is constant along their lengths and thus they are parallel to each other.

Yes, a set of lines can be parallel to each. So, if M is parallel to N and if N is parallel to P, M is parallel to P. Distance between M and P is equal to distance between M and N plus N and P.

Answer 5

Not that this is rigorous logic, but yes, yes and yes. By definition a line is always parallel to itself, if A is B then B is A, and if A is B and B is C then C is A.

Answer 6

Parallel just means that both lines have the same slope.
The rest of it drops out with a little horse sense ☺

Doug

Answer 7

yea, parallel lines just have to have the same slope, thats all

so all those answers are yes

Answer 8

Yes, it is defined to be so.