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!!