9 ES 44 : Somme des angles d'un triangle

D = (-4, -4)
F = (0, 6)
E = (8, -4)
poly1, c, a, b = Polygon(D, F, E)
D_1 = Point(c)
E_1 = Point(b)
F_1 = Point(b)
G = Point(a)
H = Point(a)
I = Point(c)
poly2, b_1, i, h = Polygon(I, H, F)
poly3, e, d, a_1 = Polygon(D_1, D, E_1)
poly4, g, f, c_1 = Polygon(F_1, E, G)
α = Angle(E_1, D, D_1)
β = Angle(I, F, H)
γ = Angle(G, E, F_1)
J = (-4, -4)
u = Vector(D, J)
D' = Translate(D_1, u)
A' = Translate(D, u)
E' = Translate(E_1, u)
poly3', e', d', a' = Polygon(D', A', E')
k = Circle(J, D')
K = Point(k)
δ = Angle(K, J, D')
D'' = Rotate(D', -δ, J)
A'' = Rotate(A', -δ, J)
E'' = Rotate(E', -δ, J)
poly3'', e'', d'', a'' = Polygon(D'', A'', E'')
j = Segment(D_1, E_1)
ε = Angle(E'', J, K)
L = (8, -4)
v = Vector(E, L)
F' = Translate(F_1, v)
C' = Translate(E, v)
G' = Translate(G, v)
poly4', g', f', c' = Polygon(F', C', G')
p = Circle(L, G')
M = Point(p)
ζ = Angle(M, L, G')
F'' = Rotate(F', -ζ, L)
C'' = Rotate(C', -ζ, L)
G'' = Rotate(G', -ζ, L)
poly4'', g'', f'', c'' = Polygon(F'', C'', G'')
η = Angle(M, L, F'')
l = Segment(F_1, G)
N = (0, 6)
w = Vector(F, N)
I' = Translate(I, w)
H' = Translate(H, w)
B' = Translate(F, w)
poly2', b', i', h' = Polygon(I', H', B')
q = Circle(N, H')
O = Point(q)
θ = Angle(O, N, H')
I'' = Rotate(I', -θ, N)
H'' = Rotate(H', -θ, N)
B'' = Rotate(B', -θ, N)
poly2'', b'', i'', h'' = Polygon(I'', H'', B'')
ι = Angle(I'', N, O)
m = Segment(I, H)
poly5, e_1, d_1, i_1, h_1, g_1, f_1 = Polygon(E_1, D_1, I, H, G, F_1)
P = (6, -8)
Q = (16, -8)
n = Line(P, Q)