A piece of land was left to two sisters,Ella and Bella,by their parents in their will.The land was shaped as an irregular quadrilateral (ABCD is and irregular quadrilateral with E as a point where the two diagonals of the quadrilateral meets).The will declared that the land should be divided equally among the two daughters.Ella suggested dividing the land into four regions by constructing the two diagonals.Ella would take two regions (AED and BEC),leaving Bella with the regions ABE and CED.Bella thought that seemed fair until she talked to her lawyer and discovered that the sums of the regions were not equal.When she pressed Ella ,Ella replied,"That's true ,but the products of the region are equal!"Bella did not know what to do.
Are the products of the region equal?Model this problem on sketchpad and find out whether Ella's claim is true.If it is true ,prove it ,if not ,explain why not?