Τα πολύγωνα ΑΒΓΔΕ και Α'Β΄Γ΄ΔΈ΄ λέγονται όμοια γιατί έχουν :

'Ολες \;  τις \;  γωνίες \;  τους  \; ίσες \;  (\hat{Α} =\hat{ Α'}, \;  \hat{Β} = \hat{Β'},  \; \hat{\Gamma} = \hat{\Gamma'},  \;  \hat{\Delta} = \hat{\Delta'},  \;   \hat{Ε} = \hat{Ε'})

1)

2)

ΑΡΑ

αρχή

Α = (-3.488263835993838, 4.341847392161627)
Β = (-2.404397050482132, 4.855257974772439)
Γ = (-1.0353021635199742, 4.246771358344811)
Δ = (-1.6628039867109625, 2.85866126461929)
Ε = (-3.260081354833478, 2.896691678146017)
πολύγ1, α, β, γ, δ, ε = Polygon(Α, Β, Γ, Δ, Ε)
n = 2 (slider from 0.1 to 8, step 0.1)
A' = (-0.3697699268022584, 4.303816978634902)
a = Line(A', α)
c = Circle(A', (n * α))
B' = Intersect(c, a, 2)
ζ = Angle(Ε, Α, Β)
η = Angle(Δ, Ε, Α)
θ = Angle(Γ, Δ, Ε)
ι = Angle(Β, Γ, Δ)
κ = Angle(Α, Β, Γ)
b = Line(B', β)
d = Circle(B', (n * β))
Γ' = Intersect(d, b, 2)
e = Line(Γ', γ)
f = Circle(Γ', (n * γ))
Δ' = Intersect(f, e, 2)
g = Line(Δ', δ)
h = Circle(Δ', (n * δ))
Ε' = Intersect(h, g, 2)
πολύγ2, ζ_1, η_1, θ_1, ι_1, κ_1 = Polygon(A', B', Γ', Δ', Ε')
λ = Angle(Ε', A', B')
μ = Angle(Δ', Ε', A')
ν = Angle(Γ', Δ', Ε')
ξ = Angle(B', Γ', Δ')
ο = Angle(A', B', Γ')
κείμενο14: "Ο αριθμός " + n + " λέγεται λόγος ομοιότητας."
j = false
k = false
l = false
m = false
o = false
p = false
q = false
r = false
s = false
t = false
u = false
v = false
w = false
i = false
z: (n * round((α * 100)) / 100)
a_1: (n * round((β * 100)) / 100)
b_1: (n * round((γ * 100)) / 100)
c_1: (n * round((δ * 100)) / 100)
d_1: (n * round((ε * 100)) / 100)
κείμενο1: "ΑΒ = " + (LaTeX[α]) + ",  \; Α'Β' = " + (LaTeX[z]) + ""
κείμενο3: "ΒΓ = " + (LaTeX[β]) + ",  \; Β'Γ' = " + (LaTeX[a_1]) + ""
κείμενο5: "ΓΔ = " + (LaTeX[γ]) + ", \; Γ'Δ' = " + (LaTeX[b_1]) + ""
κείμενο7: "ΔΕ = " + (LaTeX[δ]) + ", \; Δ'Ε' = " + (LaTeX[c_1]) + ""
κείμενο9: "EA = " + (LaTeX[ε]) + ",  \; Ε'Α' = " + (LaTeX[d_1]) + ""
κείμενο2: "Άρα \;   \; \frac{A'B'}{AB}=\frac{" + (LaTeX[z]) + "}{" + (LaTeX[α]) + "}=" + (LaTeX[n]) + " \;  \; δηλαδή \;  \; Α'Β' = " + (LaTeX[n]) + " ΑΒ "
κείμενο4: "Άρα \;  \; \frac{Β΄Γ΄}{ΒΓ}=\frac{" + (LaTeX[a_1]) + "}{" + (LaTeX[β]) + "}=" + (LaTeX[n]) + " \;  \; δηλαδή \;  \; Β'Γ' = " + (LaTeX[n]) + "  \; ΒΓ"
κείμενο6: "Άρα  \;  \; \frac{Γ΄Δ΄}{ΓΔ}=\frac{" + (LaTeX[b_1]) + "}{" + (LaTeX[γ]) + "}=" + (LaTeX[n]) + " \;  \;  δηλαδή\;  \; Γ'Δ' = " + (LaTeX[n]) + " \; ΓΔ "
κείμενο8: "Άρα  \;  \;\frac{Δ΄Ε΄}{ΔΕ}=\frac{" + (LaTeX[c_1]) + "}{" + (LaTeX[δ]) + "}=" + (LaTeX[n]) + " \;  \; δηλαδή \;  \;  Δ'Ε' = " + (LaTeX[n]) + " \; ΔΕ "
κείμενο10: "Άρα  \;  \;\frac{Ε΄Α΄}{ΕΑ}=\frac{" + (LaTeX[d_1]) + "}{" + (LaTeX[ε]) + "}=" + (LaTeX[n]) + " \;  \; δηλαδή \;  \;  Ε'Α' = " + (LaTeX[n]) + " \; ΕΑ "
κείμενο13: "Όλες \;  τις \;  πλευρές \;  τους  \; ανάλογες  \; \left(  \frac{Α'Β'}{ΑΒ} = \frac{Β'Γ'}{ΒΓ} = \frac{Γ'Δ'}{ΓΔ} = \frac{Δ'Ε'}{ΔΕ}  = \frac{Ε'Α'}{ΕΑ} = " + (LaTeX[n]) + "\right) "