AB'/AB= aire(AB'C)/aire(ABC)
par le lemme des proportions 

Montrer AB'/AB=AC'/AC ?

aire(AB'C)= aire (AB'C')+ aire (CB'C') 
aire(ABC')= aire (AB'C')+ aire(BC'B')
et  aire (CB'C')=aire(BC'B')
par le lemme du trapèze

demo étape 1

demo étape 3

demo étape 2

AC'/AC= aire(ABC')/aire(ABC)
par le lemme des proportions

A = (-0.12, 4.72)
B = (-2.62, -2.68)
C = (7.36, -2.82)
poly1, c, a, b = Polygon(A, B, C)
B' = Point(c)
d = Line(B', a)
C' = Intersect(d, b)
e = Segment(A, B)
f = Segment(B, C)
g = Segment(C, A)
h = Segment(B', C')
poly2, c', a_1, b' = Polygon(A, B', C')
poly3, c'_1, b_1, b'_1 = Polygon(B, B', C')
poly4, c'_2, b'_2, c_1 = Polygon(B', C, C')
i = Line(C', e)
D = Intersect(i, f)
j = false
k = false
t1, c_2, j_2, l = Polygon(A, B', C)
m = false
t2, m_2, a_2, n = Polygon(A, C', B)