Results 1 to 5 of 5

Math Help - Parallel Lines intersect in Square

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    14

    Parallel Lines intersect in Square

    Hey guys, I have an idea on how to do this problem for certain cases - does anyone know how to show this for a general case (since thats what its asking for I think):

    "If we have 4 points A,B,C, D which are given on a straight line (in that order), show how to construct a pair of paralllel lines through 'A' and 'B' and another pair of parallel lines through 'C' and 'D' so that the 4 lines intersect in a square"
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Jonboy's Avatar
    Joined
    May 2007
    From
    South Point
    Posts
    193
    For these lines to intersect, they must not be vertical neither horizontal. So it seems by inductive reasoning. Thus they must be oblique or slanted parallel lines.

    With a quick sketch, the attachment of this post is what I have in mind.
    Attached Thumbnails Attached Thumbnails Parallel Lines intersect in Square-square-2.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by furnis1 View Post
    Hey guys, I have an idea on how to do this problem for certain cases - does anyone know how to show this for a general case (since thats what its asking for I think):

    "If we have 4 points A,B,C, D which are given on a straight line (in that order), show how to construct a pair of paralllel lines through 'A' and 'B' and another pair of parallel lines through 'C' and 'D' so that the 4 lines intersect in a square"
    If the resulting figure is to be a square, then the A,B,C,D must be equally spaced.

    Get the midpoint of BC. Call it M.
    With M as center, draw semicircles with A and B. (A and D must be on the larger semicircle, while B and C must be on the smaller semicircle.)

    Draw a line through M that is perpendicular to the original line. This line will bisect the two semicircles.

    Draw a line through A that will pass through the the point of intersection of the larger semicircle and the perpendicular line from M.
    Do that too from D.

    Draw a line through B that will pass through the the point of intersection of the smaller semicircle and the perpendicular line from M.
    Do that too from C.

    What is the figure formed now by those four lines?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2008
    Posts
    14
    Quote Originally Posted by ticbol View Post
    If the resulting figure is to be a square, then the A,B,C,D must be equally spaced.

    Get the midpoint of BC. Call it M.
    With M as center, draw semicircles with A and B. (A and D must be on the larger semicircle, while B and C must be on the smaller semicircle.)

    Draw a line through M that is perpendicular to the original line. This line will bisect the two semicircles.

    Draw a line through A that will pass through the the point of intersection of the larger semicircle and the perpendicular line from M.
    Do that too from D.

    Draw a line through B that will pass through the the point of intersection of the smaller semicircle and the perpendicular line from M.
    Do that too from C.

    What is the figure formed now by those four lines?


    wow! thanks for the help you made it so easy. and yes it works out perfect! thanks again
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by furnis1 View Post
    Hey guys, I have an idea on how to do this problem for certain cases - does anyone know how to show this for a general case (since thats what its asking for I think):

    "If we have 4 points A,B,C, D which are given on a straight line (in that order), show how to construct a pair of paralllel lines through 'A' and 'B' and another pair of parallel lines through 'C' and 'D' so that the 4 lines intersect in a square"
    1. It doesn't matter how the 4 points are placed on the line segment. If the order is A, B, C, D then you always can construct a square.

    2. The vertices of the square are located on semi-circles over AC, AD, BC, BD.

    3. I haven't found the most important property to place one vertix definitely on it's semi-circle.
    Attached Thumbnails Attached Thumbnails Parallel Lines intersect in Square-quadrt_ausparall.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 19th 2011, 02:04 AM
  2. Replies: 6
    Last Post: February 24th 2011, 01:26 AM
  3. Do these lines intersect? If so...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 8th 2010, 11:48 AM
  4. Replies: 1
    Last Post: March 14th 2010, 01:22 PM
  5. Replies: 2
    Last Post: January 25th 2009, 08:41 PM

Search Tags


/mathhelpforum @mathhelpforum