Base

Lorsqu'on déplace le point C, l'aire du triangle ne varie pas.
Lorsqu'on déplace les points A ou B, l'aire du triangle  varie.

A

B

C

Solution

Lorsqu'un  \; sommet  \; se  \; déplace \;  parallélement  \; à \; sa \; base,  \;son  \;aire  \;ne \; change  \;pas.

A = (-0.16, -3.52)
B = (8.02, -2.26)
a = Line(A, B)
C = (1.2, 3.48)
b = Line(C, a)
D = Point(b)
poly1, b_1, d, a_1 = Polygon(D, A, B)
c = OrthogonalLine(D, b)
E = Intersect(a, c)
e = Segment(D, E)
G = Midpoint(d)
f = Segment(A, B)
texte1: "Hauteur = " + (LaTeX[e]) + "  \; cm"
texte3: "Base = " + (LaTeX[f]) + " \;  cm"
texte4: "Aire=" + (LaTeX[poly1]) + "  \; cm²"
g = Circle(E, 0.5)
h = Line(A, B)
F = Intersect(g, h, 2)
H = Intersect(g, e, 1)
k = Circle(E, 2)
K = Intersect(k, h, 1)
p = Circle(B, 2)
L = Intersect(p, h, 2)
q = Circle(If[x(K) < x(A), E, A], 2)
M = Intersect(q, h, 1)
N = Point(h)
O = Point(h)
l = Segment(N, O)
r = Circle(E, 0.5)
I = Intersect(r, e)
J, P = Intersect(r, l)
i = OrthogonalLine(P, l)
j = OrthogonalLine(I, e)
Q = Intersect(i, j)
poly2, i_1, q_1, p_1, e_1 = Polygon(I, Q, P, E)
R = Intersect(e_1, i_1)
s = Circle(R, 3)
m = Line(D, R)
S = Intersect(s, m, 1)
n = OrthogonalLine(R, m)
t = Circle(R, 0.5)
T = Intersect(t, n, 1)
c_1 = OrthogonalLine(T, n)
d_1 = OrthogonalLine(S, m)
U = Intersect(c_1, d_1)
o = false