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Quadrilateral help please!

  1. Oct 6, 2008 #1
    Show that for any quadrilateral(convex or not), the lines containing the diagonals intersect.

    How would I prove this?
    I know that

    1) A and B are on the same side of the line CD
    2) B and C are on the same side of the line DA
    3) C and D are on the same side of the line AB
    4) D and A are on the same side of the line BC

    With this being said, is this a good proof?

    Let ABCD be a quadrilateral. By condition 1 and 2 from above we know that B is in the interior of angle ADC and the ray DB intersects AC at point P. Also that A is in the interior of angle BCD and that ray CA intersects line BD at point Q. Since line DB intersect AC at point P and also at point Q, P=Q. Since P lies on AC and Q lies on BD then AC and BD have a point in common which means that the quadrilateral satisfies all the conditions of being a convex qualdrilateral also.


    Thanks for the help!!
     
  2. jcsd
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