N

(MN)//(BC)

M

Que\ constate-t-on\ pour\ les\ trois\ quotients\ ?

C

A

B

Théorème\ de\ Thalès

Quotients\ calculés\ par\ Geogebra:

A = (1.9772590899974507, 0.789808430492058)
B = (1.394316607461545, -2.358080975201833)
C = (5.1251484956913425, -2.3580809752018315)
a = Line(A, B)
b = Line(A, C)
M = Point(a)
c = Line(B, C)
d = Line(M, c)
N = Intersect(b, d)
e = Segment(A, M)
f = Segment(A, B)
g = Segment(A, N)
h = Segment(A, C)
AM = Distance(A, M)
AB = Distance(A, B)
AN = Distance(A, N)
AC = Distance(A, C)
texte7: "AM=" + (LaTeX[AM]) + ""
texte8: "AB=" + (LaTeX[AB]) + ""
texte9: "AN=" + (LaTeX[AN]) + ""
texte10: "AC=" + (LaTeX[AC]) + ""
q_1: AM / AB
q_2: AN / AC
MN = Distance(M, N)
BC = Distance(B, C)
q_3: MN / BC
texte11: "\frac{AM}{AB}\approx " + (LaTeX[q_1]) + ""
texte12: "\frac{AN}{AC}\approx " + (LaTeX[q_2]) + ""
texte13: "\frac{MN}{BC}\approx" + (LaTeX[q_3]) + ""