# Coxeter- Theorem 2.24

- Author:
- AndrewLyon

- Topic:
- Geometry

2.24

*There exist four coplanar points of which no three are collinear.*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*EA*and*EC*containing also*B*and*D*, respectively, as in the figure provided. The four distinct points*A,B,C,D*have the desired property of noncollinearity. For instance, if the three points*A,B,C*were collinear,*E*(on*AB*) would be collinear with all of them, and*EA*would be the same line as*EC*, contradicting our assumption that these two lines are distinct.