reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th39:
  parallelogram a,b,c,d implies not a,b,x are_collinear or not c,d,
  x are_collinear
proof
  assume
A1: parallelogram a,b,c,d;
  then
A2: c <>d by Th36;
  ( not a,b,c are_collinear)& a,b // c,d by A1;
  hence thesis by A2,Th28;
end;
