theorem Th50:
  not b,b9,c are_collinear & parallelogram a,a9,b,b9 &
  parallelogram a,a9,c,c9 implies parallelogram b,b9,c,c9
proof
  assume that
A1: not b,b9,c are_collinear and
A2: parallelogram a,a9,b,b9 and
A3: parallelogram a,a9,c,c9;
A4: a,a9 // c,c9 by A3;
  a<>a9 & a,a9 // b,b9 by A2,Th36;
  then
A5: b,b9 // c,c9 by A4,Def1;
  b,c // b9,c9 by A2,A3,Th49;
  hence thesis by A1,A5;
end;
