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Math Help - Parellel lines,

  1. #1
    Junior Member
    Joined
    Jan 2009
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    57

    Parellel lines,

    Hi,

    Why does it naturally follow from

    tan (\alpha - \beta) = \frac{tan \alpha - tan \beta}{1+ tan \alpha   tan \beta}

    That lines having the same slope are parellel?
    Apparently the same applies for cot and perpendicular lines.

    I don't see it.

    Thanks
    Regards
    Craig.
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  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
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    Florida
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    Let a and b be the angle each line makes with the horizontal

    The slope of a line m = dy/dx = tan(a) or tan(b)

    if the lines have the same slope tana = tanb

    therefore tan(a-b) = 0

    a-b = 0

    a = b

    i.e the lines are parallel as they make the the same angle with respect to the horizontal
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