parallel lines and a plane

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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Explain why two parallel lines define a plane.



If I hold two pencils so that they’re parallel, there’s only one position in which a plane can rest on both pencils.But can someone give me a more valid reason? Should I use definition of a plane?










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  • 3




    Because three points define a plane.
    – Mauro ALLEGRANZA
    Sep 10 at 12:33











  • 2 parallel lines in a flat space define a plane. On a curved manifold they don't - e.g. lines of longitude.
    – Paul Childs
    Sep 10 at 12:39










  • Right, by definition of a plane that is true. But the explanation can't be that simple, right? If we are talking about parallel lines, how do they define a plane? How do we know they lie on the same plane?
    – Donna
    Sep 10 at 12:43










  • @Donna They do since being parallel requires the lines to be co-planar.
    – Rushabh Mehta
    Sep 10 at 13:06










  • Thank you! I appreciate all the help you have all given me :)
    – Donna
    Sep 10 at 13:35














up vote
0
down vote

favorite












Explain why two parallel lines define a plane.



If I hold two pencils so that they’re parallel, there’s only one position in which a plane can rest on both pencils.But can someone give me a more valid reason? Should I use definition of a plane?










share|cite|improve this question



















  • 3




    Because three points define a plane.
    – Mauro ALLEGRANZA
    Sep 10 at 12:33











  • 2 parallel lines in a flat space define a plane. On a curved manifold they don't - e.g. lines of longitude.
    – Paul Childs
    Sep 10 at 12:39










  • Right, by definition of a plane that is true. But the explanation can't be that simple, right? If we are talking about parallel lines, how do they define a plane? How do we know they lie on the same plane?
    – Donna
    Sep 10 at 12:43










  • @Donna They do since being parallel requires the lines to be co-planar.
    – Rushabh Mehta
    Sep 10 at 13:06










  • Thank you! I appreciate all the help you have all given me :)
    – Donna
    Sep 10 at 13:35












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Explain why two parallel lines define a plane.



If I hold two pencils so that they’re parallel, there’s only one position in which a plane can rest on both pencils.But can someone give me a more valid reason? Should I use definition of a plane?










share|cite|improve this question















Explain why two parallel lines define a plane.



If I hold two pencils so that they’re parallel, there’s only one position in which a plane can rest on both pencils.But can someone give me a more valid reason? Should I use definition of a plane?







plane-geometry






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edited Sep 10 at 18:06

























asked Sep 10 at 12:32









Donna

156




156







  • 3




    Because three points define a plane.
    – Mauro ALLEGRANZA
    Sep 10 at 12:33











  • 2 parallel lines in a flat space define a plane. On a curved manifold they don't - e.g. lines of longitude.
    – Paul Childs
    Sep 10 at 12:39










  • Right, by definition of a plane that is true. But the explanation can't be that simple, right? If we are talking about parallel lines, how do they define a plane? How do we know they lie on the same plane?
    – Donna
    Sep 10 at 12:43










  • @Donna They do since being parallel requires the lines to be co-planar.
    – Rushabh Mehta
    Sep 10 at 13:06










  • Thank you! I appreciate all the help you have all given me :)
    – Donna
    Sep 10 at 13:35












  • 3




    Because three points define a plane.
    – Mauro ALLEGRANZA
    Sep 10 at 12:33











  • 2 parallel lines in a flat space define a plane. On a curved manifold they don't - e.g. lines of longitude.
    – Paul Childs
    Sep 10 at 12:39










  • Right, by definition of a plane that is true. But the explanation can't be that simple, right? If we are talking about parallel lines, how do they define a plane? How do we know they lie on the same plane?
    – Donna
    Sep 10 at 12:43










  • @Donna They do since being parallel requires the lines to be co-planar.
    – Rushabh Mehta
    Sep 10 at 13:06










  • Thank you! I appreciate all the help you have all given me :)
    – Donna
    Sep 10 at 13:35







3




3




Because three points define a plane.
– Mauro ALLEGRANZA
Sep 10 at 12:33





Because three points define a plane.
– Mauro ALLEGRANZA
Sep 10 at 12:33













2 parallel lines in a flat space define a plane. On a curved manifold they don't - e.g. lines of longitude.
– Paul Childs
Sep 10 at 12:39




2 parallel lines in a flat space define a plane. On a curved manifold they don't - e.g. lines of longitude.
– Paul Childs
Sep 10 at 12:39












Right, by definition of a plane that is true. But the explanation can't be that simple, right? If we are talking about parallel lines, how do they define a plane? How do we know they lie on the same plane?
– Donna
Sep 10 at 12:43




Right, by definition of a plane that is true. But the explanation can't be that simple, right? If we are talking about parallel lines, how do they define a plane? How do we know they lie on the same plane?
– Donna
Sep 10 at 12:43












@Donna They do since being parallel requires the lines to be co-planar.
– Rushabh Mehta
Sep 10 at 13:06




@Donna They do since being parallel requires the lines to be co-planar.
– Rushabh Mehta
Sep 10 at 13:06












Thank you! I appreciate all the help you have all given me :)
– Donna
Sep 10 at 13:35




Thank you! I appreciate all the help you have all given me :)
– Donna
Sep 10 at 13:35










1 Answer
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I would like to expand on the comments a little.



Three points indeed define a plane, but if you have two lines, $L1$ and $L2$ you have lots of choices for those three points. Pick any two points on $L1$ to start, and then we need to pick one point on $L2$ to define our plane. If the lines are not parallel, then your choice matters a lot! But if the lines are parallel, then it doesn't matter which point you pick on $L2$ -- every choice gives the same plane.






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    1 Answer
    1






    active

    oldest

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    1 Answer
    1






    active

    oldest

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    active

    oldest

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    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    I would like to expand on the comments a little.



    Three points indeed define a plane, but if you have two lines, $L1$ and $L2$ you have lots of choices for those three points. Pick any two points on $L1$ to start, and then we need to pick one point on $L2$ to define our plane. If the lines are not parallel, then your choice matters a lot! But if the lines are parallel, then it doesn't matter which point you pick on $L2$ -- every choice gives the same plane.






    share|cite|improve this answer
























      up vote
      1
      down vote



      accepted










      I would like to expand on the comments a little.



      Three points indeed define a plane, but if you have two lines, $L1$ and $L2$ you have lots of choices for those three points. Pick any two points on $L1$ to start, and then we need to pick one point on $L2$ to define our plane. If the lines are not parallel, then your choice matters a lot! But if the lines are parallel, then it doesn't matter which point you pick on $L2$ -- every choice gives the same plane.






      share|cite|improve this answer






















        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        I would like to expand on the comments a little.



        Three points indeed define a plane, but if you have two lines, $L1$ and $L2$ you have lots of choices for those three points. Pick any two points on $L1$ to start, and then we need to pick one point on $L2$ to define our plane. If the lines are not parallel, then your choice matters a lot! But if the lines are parallel, then it doesn't matter which point you pick on $L2$ -- every choice gives the same plane.






        share|cite|improve this answer












        I would like to expand on the comments a little.



        Three points indeed define a plane, but if you have two lines, $L1$ and $L2$ you have lots of choices for those three points. Pick any two points on $L1$ to start, and then we need to pick one point on $L2$ to define our plane. If the lines are not parallel, then your choice matters a lot! But if the lines are parallel, then it doesn't matter which point you pick on $L2$ -- every choice gives the same plane.







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        share|cite|improve this answer



        share|cite|improve this answer










        answered Sep 10 at 13:58









        dbx

        1,470211




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