thales
Author: Enric Brasó

El recíproc del teorema de Thales

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El teorema de TALES

Mostra/Amaga els triangles ABC i AB'C'

Ara r i r_1 són paral·leles!

Mou els punts B', C', A,  B i C .
Aconsegueix que les tres proporcions siguin iguals.
Com estan col·locades les rectes? 
Comprova-ho en una altra posició. 

C_1 = (6.4, 1)
C_0 = (6, 1)
B = (-1.8832117507148796, 0.13432917475737374)
A = (-4.2, -1)
c = Segment(A, B)
a_1 = Line(A, B)
B' = Point(a_1)
c' = Segment(A, B')
C = (-2.6541499128030486, 0.736037008582286)
b = Segment(A, C)
b_1 = Line(A, C)
C' = Point(b_1)
b' = Segment(A, C')
B_1 = (6.4, 3)
B_0 = (6, 3)
b_2 = Segment(A, C)
A_1 = (6.4, 5)
r = Line(B, C)
r_1 = Line(B', C')
a = Segment(C, B)
a' = Segment(C', B')
text1: "a       " + a
text2: "a'       " + a'
text3: "b      " + b
A_0 = (6, 5)
A_2 = Rotate(A_1, 2 * 3.14 * a / a', A_0)
f = CircleSector(A_0, A_1, A_2)
e = Circle(A_0, 0.4)
B_2 = Rotate(B_1, 2 * 3.14 * b_2 / b', B_0)
g = Circle(B_0, B_1)
h = CircleSector(B_0, B_1, B_2)
text4: "b'      " + b'
C_2 = Rotate(C_1, 2 * 3.14 * c / c', C_0)
k = CircleSector(C_0, C_1, C_2)
p = Circle(C_0, C_1)
text5: "c        " + c
text6: "c'      " + c'
text8: "" + (c' / c)
text12: " " + (b' / b)
text13: " " + (a' / a)
i = Segment(A, B)
poly1, c_2, a_2, b_3 = Polygon(A, B, C)
poly2, c'_1, a_3, b'_1 = Polygon(A, B', C')
j = false
pe = Slope(r)
pe_1 = Slope(r_1)