ÁNGULOS ALTERNOS INTERNOS
Author: Marco

$Simulación:Ángulos\,\, Alternos\,\, Internos$

$l_2$

$l_3$

$l_2||l_3$

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$Marco \,\,Gutiérrez\,\,Montenegro$
                 $vgutierrez\@itcr.ac.cr$
                                         $TEC\,\,2012$

$\fbox{Teorema}$
$Si\,\,\,una \,\,\, línea \,\,\, recta\,\,\, l_1\,\,\, interseca\,\,\,a \,\,\,dos \,\,\,líneas\,\,\, rectas\,\,\,paralelas\,\,\,l_2$
$y \,\,\,l_3,entonces \,\,\, los \,\,\,\,ángulos\,\,\,alternos\,\,\,internos\,\,\,tienen\,\,\,\,la \,\,\,misma$
$medida.$

$l_1$

A = (-3, 1)
B = (4, 1)
a = Line(A, B)
C = (-0.5629147485536848, -2.162701504054021)
b = Line(C, a)
D = Point(a)
E = Point(b)
c = Line(D, E)
F = Point(c)
G = Point(c)
d = Segment(F, G)
H = Point(a)
I = Point(a)
e = Segment(H, I)
J = Point(b)
K = Point(b)
f = Segment(J, K)
g = 10 (slider from 0 to 10, step 0.0010)
L = (6.383254740085255, -0.3047595131718716)
h = Line(L, d)
i = Line(L, f)
M = Point(h)
N = Point(i)
O = Point(i)
P = Point(h)
Q = Point(Segment[L, P], g)
R = Point(Segment[L, M], g)
S = Point(Segment[L, N], g)
T = Point(Segment[L, O], g)
j = Segment(L, Q)
k = Segment(L, T)
l = Segment(L, S)
m = Segment(L, R)
U = Point(Segment[D, L], g - 2)
u = Vector(D, U)
polígono1, d_1, h_1, e_1 = Polygon(H, E, D)
H' = Translate(H, u)
E' = Translate(E, u)
D' = Translate(D, u)
polígono1', d', h', e' = Polygon(H', E', D')
α = Angle(H', U, E')
β = Angle(H, D, E)
V = Point(Segment[E, L], g - 4)
v = Vector(E, V)
polígono2, d_2, e_2, k_1 = Polygon(E, K, D)
E'_1 = Translate(E, v)
K' = Translate(K, v)
D'_1 = Translate(D, v)
polígono2', d'_1, e'_1, k' = Polygon(E'_1, K', D'_1)
γ = Angle(K', V, D'_1)
δ = Angle(K, E, D)
ε = Angle(E, D, I)
W = Point(Segment[D, L], g - 6)
w = Vector(D, W)
polígono3, i_1, e_3, d_3 = Polygon(E, D, I)
E'_2 = Translate(E, w)
D'_2 = Translate(D, w)
I' = Translate(I, w)
polígono3', i', e'_2, d'_2 = Polygon(E'_2, D'_2, I')
ζ = Angle(E'_2, W, I')
η = Angle(D, E, J)
Z = Point(Segment[E, L], g - 8)
z = Vector(E, Z)
polígono4, d_4, j_1, e_4 = Polygon(J, E, D)
J' = Translate(J, z)
E'_3 = Translate(E, z)
D'_3 = Translate(D, z)
polígono4', d'_3, j', e'_3 = Polygon(J', E'_3, D'_3)
θ = Angle(D'_3, Z, J')
t = If(g < 10, 0.5, 0)