Glide Reflection Property

Glide Transformation

Reference angles

A = (4.30196427805549, 6.542110898337063)
B = (4.308022429000383, 10.424191664147347)
C = (7.687379854263281, 10.430635442366524)
D = (7.3680224290003915, 8.919079761922413)
E = (5.348022429000385, 8.919079761922413)
F = (5.548022429000379, 6.439079761922423)
poly1, a, b, c, d, e, f = Polygon(A, B, C, D, E, F)
G = (12.139548511750428, 13.86518573653755)
H = (3.1465729635016957, -1.6896137460792415)
g = Line(G, H)
I = (17.813311148953638, 11.929619384491403)
J = (17.813311148953602, 1.536566887352389)
h = Line(I, J)
K = (19.307994553366665, -2.465717430620603)
L = (31.713427227157347, 4.70274752078402)
i = Line(K, L)
A' = Mirror(A, g)
B' = Mirror(B, g)
C' = Mirror(C, g)
D' = Mirror(D, g)
E' = Mirror(E, g)
F' = Mirror(F, g)
poly1', a', b', c', d', e', f' = Polygon(A', B', C', D', E', F')
A'' = Mirror(A', h)
B'' = Mirror(B', h)
C'' = Mirror(C', h)
D'' = Mirror(D', h)
E'' = Mirror(E', h)
F'' = Mirror(F', h)
poly1'', a'', b'', c'', d'', e'', f'' = Polygon(A'', B'', C'', D'', E'', F'')
A''' = Mirror(A'', i)
B''' = Mirror(B'', i)
C''' = Mirror(C'', i)
D''' = Mirror(D'', i)
E''' = Mirror(E'', i)
F''' = Mirror(F'', i)
poly1''', a''', b''', c''', d''', e''', f''' = Polygon(A''', B''', C''', D''', E''', F''')
M = Intersect(j, g)
N = Intersect(j, h)
O = Intersect(i, j)
k = Circle(M, 1)
p = Circle(N, 1)
q = Circle(O, 1)
P = Intersect(k, j, 2)
Q = Intersect(k, g, 1)
R = Intersect(p, j, 2)
S = Intersect(p, h, 1)
T = Intersect(q, j, 2)
U = Intersect(q, i, 2)
α = Angle(P, M, Q)
β = Angle(R, N, S)
γ = Angle(T, O, U)
AngleSum: α + β + γ
text1: "Angle Sum (Between lines and a horizontal) = " + α + "+" + β + "+" + γ + " = " + AngleSum + ""
V = Intersect(g, i)
W = Intersect(h, i)
r = Circle(V, 2)
s = Circle(W, 2)
Z = Intersect(s, i, 2)
A_1 = Intersect(s, h, 1)
B_1 = Intersect(r, i, 2)
C_1 = Intersect(r, g, 1)
δ = Angle(B_1, V, C_1)
ε = Angle(Z, W, A_1)
AngleSum2: δ + ε
text2: "Angle Sum (between 1st -3rd and 2nd - 3rd mirror lines respectively) = " + δ + "+" + ε + "=" + AngleSum2 + ""
D_1 = Intersect(g, h)
E_1 = Intersect(h, i)
F_1 = Intersect(g, i)
t = Circle(F_1, 2)
c_1 = Circle(E_1, 2)
d_1 = Circle(D_1, 2)
G_1 = Intersect(t, g, 1)
H_1 = Intersect(t, i, 2)
I_1 = Intersect(c_1, h, 1)
J_1 = Intersect(c_1, i, 1)
K_1 = Intersect(d_1, g, 2)
L_1 = Intersect(d_1, h, 2)
ζ = Angle(I_1, E_1, J_1)
η = Angle(H_1, F_1, G_1)
θ_1 = Angle(K_1, D_1, L_1)
l = Line(B, A)
m = Line(C''', B''')
θ = Angle(m, l)
Ans = If(θ < 91, If[θ > 89, "Glide Transformation", ""], "")
text3: "" + Ans + ""
b_1 = Line(F, n)
a_1 = OrthogonalLine(F''', n)
M_1 = Intersect(b_1, a_1)
ι = Angle(F, M_1, F''')
e_1 = Segment(F, M_1)
f_1 = Segment(M_1, F''')
N_1 = Point(Circle[H, 2])
g_1 = Segment(H, N_1)
O_1 = Point(Circle[K, 2])
h_1 = Segment(K, O_1)
P_1 = Point(Circle[J, 2])
i_1 = Segment(J, P_1)
κ = Angle(N_1, H, G)
λ = Angle(P_1, J, I)
μ = Angle(O_1, K, L)
text5: "" + κ + "+" + μ + "=" + λ + ""
o = false