When a line intersects two parallel lines, the corresponding angle made by them 
are equal

When a line intersect two parallel lines, the alternate angles are equal.

Author- Ganesh Shettigar, GHS, Kalavara, Karnataka
License- CC BY SA 4.0

A = (1.24, -5.84)
B = (14.9, -5.84)
a = Line(A, B)
C = (0.52, -0.7)
b = Line(C, a)
D = Point(b)
E = (5.24, 2.46)
F = (10.14, -9.64)
c = Line(E, F)
G = Intersect(b, c)
H = Intersect(a, c)
α = Angle(E, G, C)
β = Angle(G, H, A)
γ = Angle(D, G, E)
δ = Angle(B, H, G)
ε = Angle(A, H, F)
ζ = Angle(H, G, D)
η = Angle(C, G, H)
θ = Angle(F, H, B)
d = Segment(C, D)
e = Segment(A, B)
f = Segment(E, F)
g = Segment(E, F)
text1: "$ ∠EGD =∠GHB=" + (LaTeX[γ]) + " $"
text2: "$ ∠DGH=∠BHF=" + (LaTeX[α]) + " $"
text3: "$ ∠EGC=∠GHA=" + (LaTeX[β]) + " $"
text4: "$ ∠CGH=∠AHF=" + (LaTeX[γ]) + " $"
n = 1 (slider from 1 to 2, step 1)
text7: "$ ∠DGH=∠GHA=" + (LaTeX[β]) + " $"
text8: "$ ∠CGH=∠GHB=" + (LaTeX[γ]) + " $"