Two sets of Cointerior Angles are shown on both diagrams below. One set is shown in blue and the other set
is shown in red.

DIAGRAM 1

DIAGRAM 2

In diagram 2, the lines are parallel. Move the parallel lines.

What do you notice about the sum of cointerior angles on parallel lines?

On Diagram 1, the lines are not parallel.

Are the cointerior angles equal?

A = (-5.029863945578234, 1.8281269841269805)
B = (4.342834467120182, 1.0159727891156427)
f = Segment(A, B)
C = (-5.007913832199549, -2.166793650793654)
D = (4.474535147392292, -0.8717369614512503)
g = Segment(C, D)
E = (-2.132448979591838, 2.5744308390022637)
F = (4.474535147392292, -4.010603174603177)
h = Segment(E, F)
G = Intersect(f, h)
H = Intersect(g, h)
α = Angle(A, G, H)
β = Angle(D, H, G)
γ = Angle(H, G, B)
δ = Angle(G, H, C)
I = (13.693582766439915, 1.213523809523806)
J = (23.132131519274385, 3.803637188208613)
i = Segment(I, J)
K = (15.230090702947852, -0.8278367346938806)
j = Line(K, i)
L = Point(j)
k = Segment(K, L)
M = (18.610408163265312, 4.615791383219951)
N = (17.644603174603184, -2.166793650793654)
l = Segment(M, N)
O = Intersect(l, i)
P = Intersect(l, k)
ε = Angle(I, O, P)
ζ = Angle(O, P, K)
η = Angle(P, O, J)
θ = Angle(L, P, O)
Z: ε + ζ
text2: "" + ζ + "+" + ε + "=" + Z + ""