A

B

Γ

E

Z

Δ

M

prwto

1o

2o

Επανεκκίνηση

\text{Έστω το ορθογώνιο τρίγωνο ΑΒΓ με } \hatΑ = 90^0

\text{i) Αν ΑΔ το ύψος του και Ε, Ζ τα μέσα των ΑΒ και ΑΓ, } \cr
 \quad \text{να αποδείξετε ότι } Ε\hatΔΖ = 90^0

\text{ii) Αν Μ το μέσο της ΕΖ να αποδείξετε ότι } ΔΜ=\frac{BΓ}{4}

j = 0 (slider from -0.05 to 16, step 0.05)
B = (7, 1)
A = (4, 1)
A' = Dilate(A, If[0 < j ≤ 1, 1 - j, 0], B)
f = Segment(A, A')
E = Midpoint(f)
D = (4, 5)
A''' = Dilate(D, If[2 < j ≤ 3, 3 - j, 0], B)
i_1 = Segment(D, A''')
m = OrthogonalLine(A, i_1)
G = Intersect(m, i_1)
A'' = Dilate(A, If[1 < j ≤ 2, 2 - j, 0], D)
h = Segment(A, A'')
F = Midpoint(h)
a = Segment(E, F)
H = Midpoint(a)
κ = Angle(G, H, D)
G'_1 = Rotate(G, If[13 < j ≤ 14, ((j - 13) * κ), κ], H)
r_1 = Segment(H, G'_1)
M = Dilate(G'_1, If[14 < j ≤ 15, 15 - j, 0], D)
c = Segment(B, D)
I = Midpoint(c)
η = Angle(B, I, D)
β = Angle(A, E, B)
g = OrthogonalLine(A, f)
C = Point(g)
α = Angle(B, A, C)
A'_1 = Rotate(A, If[3 < j ≤ 4, ((-(j - 3)) * β), β], E)
l = Segment(E, A'_1)
γ = Angle(A, F, D)
A'_2 = Rotate(A, If[4 < j ≤ 5, ((-(j - 4)) * γ), γ], F)
k = Segment(F, A'_2)
A'_3 = Dilate(A, If[5 < j ≤ 6, 6 - j, 0], G)
n = Segment(A, A'_3)
E' = Dilate(E, If[6 < j ≤ 7, 7 - j, 0], G)
p = Segment(E, E')
F' = Dilate(F, If[6 < j ≤ 7, 7 - j, 0], G)
q = Segment(F, F')
F'_1 = Dilate(F, If[7 < j ≤ 8, 8 - j, 0], E)
r = Segment(F, F'_1)
s = Segment(A, B)
t = Segment(A, D)
δ = Angle(F, G, E)
ε = Angle(B, A, D)
ζ = Angle(E, H, F)
e = Segment(I, D)
J = Midpoint(e)
θ = Angle(I, J, D)
g_1 = Segment(A, E)
j_1 = Segment(E, B)
k_1 = Segment(A, F)
l_1 = Segment(F, D)
i = Segment(D, A''')
E'_1 = Rotate(E, If[8 < j ≤ 9, ((j - 4) * ζ), ζ], H)
b = Segment(H, E'_1)
d = Segment(H, E)
G' = Dilate(G, If[9 < j ≤ 10, 10 - j, 0], H)
f_1 = Segment(G, G')
D' = Rotate(I, If[10 < j ≤ 11, ((-(j - 11)) * θ), θ], J)
h_1 = Segment(J, D')
J' = Rotate(J, If[11 < j ≤ 12, ((-(j - 11)) * θ), θ], I)
m_1 = Segment(I, J')
c_1 = Circle(I, J)
K, L = Intersect(c_1, i)
I' = Rotate(I, If[12 < j ≤ 13, ((-(j - 12)) * β), β], L)
n_1 = Segment(J', I')
p_1 = Line(D, H)
q_1 = Segment(G'_1, H)
d_1 = Circle(D, J)
N = Intersect(d_1, p_1, 2)
H' = Dilate(H, If[14 < j ≤ 15, 15 - j, 0], N)
s_1 = Segment(M, H')
H'' = Dilate(H', If[15 < j ≤ 16, 16 - j, 0], K)
t_1 = Segment(D, H'')
a_1 = Segment(J, J')
o = If(j < 3, true, false)
u: false
v: false
w: false