2.24 [i]There exist four coplanar points of which no three are collinear.[/i] PROOF. By our first three axioms, there exist two distinct lines having a common point and each containing at least two other points, say lines [i]EA[/i] and [i]EC[/i] containing also [i]B[/i] and [i]D[/i], respectively, as in the figure provided. The four distinct points [i]A,B,C,D[/i] have the desired property of noncollinearity. For instance, if the three points [i]A,B,C[/i] were collinear, [i]E[/i] (on [i]AB[/i]) would be collinear with all of them, and [i]EA[/i] would be the same line as [i]EC[/i], contradicting our assumption that these two lines are distinct.