Triángulos semejantes
Author: Miriam y Nerea

Mueve los deslizadores y podrás comprobar que los triángulos son semejantes

A

A

B

B

C

C

E

E

D

D

  \frac{ CD }{CB }=          \frac{CE }{ CA }=       \frac{ ED }{ AB }  

?

¿Cómo se puede aplicar el teorema 
de Tales con esta configuración?

Superponer los triángulos

Poner en su sitio

A = (0.1851975686131974, 3.19492363728302)
a = 3.3 (slider from 0.1 to 5, step 0.1)
c = Circle(A, a)
B = Point(c)
b = Line(B, A)
d = 4.5 (slider from 0 to 15, step 0.1)
e = Circle(A, d)
C = Point(e)
f = Line(A, C)
D_1 = Intersect(e, f, 1)
g = Line(B, C)
E = Point(f)
h = Line(E, b)
D = Intersect(g, h)
i = Segment(B, C)
j = Segment(C, D)
k = Segment(A, C)
l = Segment(C, E)
m = Segment(B, A)
n = Segment(E, D)
t: 0.001
T1: "AB = " + a
F = (2.3470670395916757, -2.435949075720102)
p = Segment(A, F)
q = Circle(A, If[t  <  p, t, p])
G, H = Intersect(q, p)
u = Vector(A, G)
poly1, c_1, b_1, a_1 = Polygon(B, A, C)
B' = Translate(B, u)
A' = Translate(A, u)
C' = Translate(C, u)
poly1', c', b', a' = Polygon(B', A', C')
poly2, c_2, e_1, d_1 = Polygon(E, D, C)
E' = Rotate(E, If[t  <  3.14, t, 3.14], C')
D' = Rotate(D, If[t  <  3.14, t, 3.14], C')
C'_1 = Rotate(C, If[t  <  3.14, t, 3.14], C')
poly2', c'_1, e', d' = Polygon(E', D', C'_1)
r = Line(C', C'_1)
s = Segment(C', C'_1)
c1 = Circle(C'_1, If[t + 3.14  <  s, t - 3.14, s])
v = Vector(C'_1, C')
E'' = Translate(E', v)
D'' = Translate(D', v)
C'_1' = Translate(C'_1, v)
poly2'', c'_1', e'', d'' = Polygon(E'', D'', C'_1')
T10: "AC = " + d
I = Midpoint(C, D)