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Sunday, November 27

  1. page Angle Bisectors and Trilinear Lines edited {trilinear_angle_bisectors1.png} Let's begin with triangle ABC, with the line through B and C …
    {trilinear_angle_bisectors1.png}
    Let's begin with triangle ABC, with the line through B and C
    being a, the line through A and C being b, and the line
    through A and B being c, as shown at left.
    {trilinear_angle_bisectors2.png}
    The equation of each side can be written as a dot product equation.
    For example, let u be a unit vector perpendicular to a. Using GeoGebra
    notation, the equation of this line is
    x(u) x + y(u) y = x(u) x(B) + y(u) y(B)
    where x(u) is the x-coordinate of vector u, and the others are defined
    accordingly.
    We want to have the side line equations written as
    x(u) x + y(u) y - x(u) x(B) - y(u) y(B) = 0
    Select any two of the side line equations, say, a and b. Add these two equations
    in the form above term by term. This results in another linear equation which
    must go through point C, since C is on side a and b.
    It just so happens that this new line with the form a - b = 0 is the angle bisector of C.

    (view changes)
    7:35 am

Friday, November 25

  1. page Trilinear Lines edited When m = n, the lines form the angle bisectors. When m = - n, the lines form the external angle bis…
    When m = n, the lines form the angle bisectors. When m = - n, the lines form the external angle bisectors.
    Click on the check box to show a line that is the sum of the lines containing the sides of the triangle.
    The Altitudes
    (view changes)
    1:52 pm
  2. page Trilinear Lines edited When m = n, the lines form the angle bisectors. When m = - n, the lines form the external angle bi…
    When m = n, the lines form the angle bisectors. When m = - n, the lines form the external angle bisectors.
    Click on the check box to show a line that is the sum of the lines containing the sides of the triangle.

    (view changes)
    1:26 pm
  3. 12:31 pm

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