Η ΑΠΟΔΕΙΞΗ ΤΟΥ ΕΥΚΛΕΙΔΗ ΓΙΑ ΤΟ ΠΥΘΑΓΟΡΕΙΟ ΘΕΩΡΗΜΑ

Τρίγωνο ΕΓΒ

Τρίγωνο ΑΓΛ

Ορθογώνιο ΔΚΒΜ

Τμήμα ΑΚ

Ορθογώνιο ΓΛΚΔ

1.    Απόδειξε οτι:    ΕΓΒ=ΑΓΛ

2.    Απόδειξε οτι:    (ΕΓΒ)=1/2(ΑΓΕΖ)  και 

                                  (ΑΓΛ)=1/2(ΓΛΚΔ)

Γ = (-0.3, 4.62)
A = (-0.26, 1)
β = Segment(Γ, A)
b = OrthogonalLine(A, β)
B = Point(b)
γ = Segment(A, B)
α = Segment(Γ, B)
α_1 = Angle(B, A, Γ)
β_1 = Angle(A, Γ, B)
ΑΓΕΖ, e, f, g, h, E, Z = Polygon(A, Γ, 4)
i = OrthogonalLine(A, α)
Δ = Intersect(i, α)
ΑΒΗΘ, j, k, l, m, Θ, H = Polygon(B, A, 4)
ΒΓΛΜ, n, p, q, r, M, Λ = Polygon(Γ, B, 4)
s = Ray(A, Δ)
K = Intersect(q, s)
t = Segment(A, K)
γ_4 = Angle(Γ, Δ, A)
ΓΛΚΔ, γ_1, δ, k_1, λ = Polygon(Γ, Δ, K, Λ)
ΔΚΜΒ, δ_1, b_1, m_1, k_2 = Polygon(Δ, B, M, K)
a_1 = Segment(E, Γ)
c_1 = Segment(E, B)
d_1 = Segment(Λ, A)
ΕΓΒ, b_2, e_1, γ_2 = Polygon(E, Γ, B)
ΑΓΛ, a_2, γ_3, λ_1 = Polygon(Γ, Λ, A)
κείμενο3: "(ΓΛΚΔ)=" + (LaTeX[ΓΛΚΔ]) + ""
κείμενο4: "(ΑΓΕΖ)=" + (LaTeX[ΑΓΕΖ]) + ""
κείμενο1: "(ΑΒΗΘ)=" + (LaTeX[ΑΒΗΘ]) + ""
κείμενο2: "(ΔΚΜΒ)=" + (LaTeX[ΔΚΜΒ]) + ""
a = false
c = false
ε = Angle(B, Γ, Λ)
η = Angle(E, Γ, A)
θ = Angle(A, B, H)
ι = Angle(B, H, Θ)
κ = Angle(Γ, Λ, M)
μ = Angle(Z, E, Γ)
ν = Angle(Γ, A, Z)
ξ = Angle(Θ, A, B)
d = false
o = false
u = false
ο = Angle(M, B, Γ)