Morley mit Winkelsubtraktion
Trick: Sqrt[3] dargestellt als Polynom a^2-3==0

source  =  
        DirectoryName[
          ToFileName["FileName" /. 
              NotebookInformation[EvaluationNotebook[]]]];
SetDirectory[source];
\(Needs["GeoBeweiser`"]
\)
clearndg[];
Clear[u1, u2, u3, x1, x2, x3, x4, x5, x6, y];
vars := {x1, x2, x3, x4, x5, x6, y};
parameters := {u1, u2, u3};

Unprotect[C, D, E];
A = point[0, 0]; B = point[u1, 0];
C = point[x5, x6];
D = point[u2, u3]; E = point[x1, x2];
F = point[x3, x4];

\(\(\( (*Verdreifachung\ des\ Winkels\ wBAD*) \)\(
\)\(Bad = sympoint[B, ppline[A, D]]

    Da = sympoint[D, ppline[A, Bad]]\)\)\)

\(\(\( (*Verdreifachung\ des\ Winkels\ wABD*) \)\(
\)\(Abd = sympoint[A, ppline[B, D]]

    Db = sympoint[D, ppline[B, Abd]]\)\)\)

\(\(\( (*Bestimme\ C*) \)\(
\)\(gleichungc = 
      intersectionpoint[ppline[A, Da], ppline[B, Db]]

    d1 = gleichungc[\([1]\)] - C[\([1]\)]

    d2 = gleichungc[\([2]\)] - C[\([2]\)]\)\)\)

\(\(\( (*Betimmung\ der\ Geradenwinkel\ \((Drittelwinkel)\)*) \)\(
\)\( (*V3 = Tan[Pi/3]*) \)\(
\)\(wA3 = p3angle[D, A, B]

    wB3 = p3angle[A, B, D]

    wC3 = p3angle[F, C, A]

    dreineu = anglesum[V3, \(-anglesum[wA3, wB3]\)] - wC3\)\)\)

\(\(\( (*Bestimme\ F*) \)\(
\)\(d3 = dreineu

    d4 = online[F, ppline[A, Bad]]\)\)\)

\(\(\(Acf = sympoint[A, ppline[C, F]]\)\(
\)
    \) (*Bestimme\ E*) \)
d5 = online[E, ppline[C, Acf]]
d6 = online[E, ppline[B, Abd]]

(* polynomials *)
polys1={d1,d2,d3,d4,d5,d6,V3^2-3
  }
polys=Map[Numerator[Together[#]] &, polys1]

InputForm[polys /. {Sqrt[3] -> a}]

con1 = 
      sqrdist[D, E] - sqrdist[E, F]

    con2 = sqrdist[D, E] - sqrdist[D, F]

{IdealMember[con1, polys, vars], IdealMember[con2, polys, vars]} // 
      Timing