Pappus's hexagon theorem
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that if A , B , C {\displaystyle A,B,C} is one set of collinear points, and a , b , c {\displaystyle a,b,c} is another set of collinear points, then the intersection points X , Y , Z {\displaystyle X,Y,Z} of line pairs A b {\displaystyle Ab} and a B , A c {\displaystyle aB,Ac} and a C , B c {\displaystyle aC,Bc} and b C {\displaystyle bC} are collinear, lying on the Pappus line. These three points are the points of intersection of the "opposite" sides of the hexagon A b C a B c {\displaystyle AbCaBc} .