Angles triangles
Author: Daniel Mentrard

I = (14, 0)
A = (-21.99285031943034, -7.1198176173480805)
B = (-2.3281743521383813, -6.829411010236174)
C = (-11.413752488925173, 8.230245901424125)
D_1 = (6, 0)
v = Vector(A, D_1)
Ver = 0 (slider from 0 to 3, step 0.2)
k: (1.0 + sgn(1.0 - Ver)) / 2.0
u: (1.0 + sgn(2.0 - Ver)) / 2.0
t: (1.0 + sgn(3.0 - Ver)) / 2.0
a_1: k * u * t
a_2: (1.0 - k) * u * t
a_3: (1.0 - k) * (1.0 - u) * t
a_4: (1.0 - k) * (1.0 - u) * (1.0 - t)
b_1: a_1 * Ver + a_2 + a_3 + a_4
B': B + v * b_1
ζ = Angle(B', D_1, I)
A': A + v * b_1
J = Rotate(B', ζ * b_1, A')
C': C + v * b_1
L = Rotate(C', ζ * b_1, A')
b_3: a_3 * (Ver - 2.0) + a_4
b_2: a_2 * (Ver - 1.0) + a_3 + a_4
z = Vector(C, D_1)
C''': C + z * b_3
B''': B + z * b_3
w = Vector(B, D_1)
C'': C + w * b_2
B'': B + w * b_2
A''': A + z * b_3
A'': A + w * b_2
δ = Angle(L, D_1, C'')
F = Rotate(A'', -(δ) * b_2, B'')
ε = Angle(F, D_1, A''')
H = Rotate(B''', -(ε) * b_3, C''')
G = Rotate(A''', -(ε) * b_3, C''')
E = Rotate(C'', -(δ) * b_2, B'')
poly1, c, a, b = Polygon(A, B, C)
α_1 = Angle(B, A, C)
β_1 = Angle(C, B, A)
γ_1 = Angle(A, C, B)
β = Angle(E, B'', F)
θ = Angle(G, C''', H)
d = Ray(D_1, I)
α = Angle(J, A', L)
T2: "α + β + θ = " + α + " + " + β + " + " + θ + " = " + (α + β + θ)
poly2, a_5, c_1, b_4 = Polygon(C, B, A)
e = Line(D_1, xAxis)
f = Circle(D_1, I)
O = Midpoint(D_1, I)
P = Mirror(O, D_1)
g = Segment(P, O)