An Geradenkreuzungen gilt:

Scheitelwinkel sind gleich groß.

Die Summe zweier Nebenwinkel beträgt 180°.

An Geradenkreuzungen mit zueinander parallelen Geraden gilt:

Stufenwinkel sind gleich groß.

Wechselwinkel sind gleich groß.

A = (-3.412098776456914, 12.069291155670852)
B = (2.62426389117902, 13.839570591852544)
a = Segment(A, B)
C = (-3.1509100071842053, 14.158801309852521)
D = (2.82741071172446, 12.098312130034486)
b = Segment(C, D)
E = (4.597690147906152, 13.955654489307081)
F = (10.227759174451206, 11.953207258216315)
c = Segment(E, F)
G = (4.5106272248152495, 12.069291155670852)
H = (10.198738200087572, 13.926633514943447)
d = Segment(G, H)
I = Intersect(a, b)
J = Intersect(c, d)
α = Angle(C, I, A)
β = Angle(D, I, B)
γ = Angle(E, J, G)
δ = Angle(H, J, E)
K = (-3.615245597002354, 6.149012385489455)
L = (2.82741071172446, 6.149012385489455)
e = Segment(K, L)
M = (5.033004763360666, 6.17803335985309)
N = (10.982304507905697, 6.17803335985309)
f = Segment(M, N)
O = (1.8116766089972596, 7.280830385671194)
P = (-2.9477631866387655, 3.1018100773078543)
g = Segment(O, P)
Q = (9.502234815360348, 7.454956231852999)
R = (5.32321450699701, 2.8986632567624144)
h = Segment(Q, R)
S = Intersect(e, g)
T = Intersect(f, h)
U = (2.7113268142699227, 4.204607103125958)
i = Line(U, e)
V = Point(i)
j = Segment(U, V)
W = Point(i)
Z = Point(i)
k = Segment(W, Z)
A_1 = Intersect(g, j)
B_1 = Intersect(h, k)
ε = Angle(O, S, K)
ζ = Angle(S, A_1, V)
η = Angle(B_1, T, N)
θ = Angle(T, B_1, W)