In a trapezium \(ABCD\), the side \(AB\) is parallel to the side \(CD\). Show that the areas of triangles \(\triangle ABC\) and \(\triangle ABD\) are equal.
9 straight lines each divide a square into two quadrilaterals, with their areas having a ratio of \(2:3\). Prove that at least three of the nine lines pass through the same point.