α

Kathetensatz

Kathetensatz

Satz des Pythagoras

Beweis wegen Ähnlichkeit:

\frac{b}{c}=\frac{p}{b}

A = Point(xAxis)
B = Point(yAxis)
c_2 = Semicircle(A, B)
C = Point(c_2)
c = Segment(A, B)
g = OrthogonalLine(C, c)
D = Intersect(g, c)
E = Point(g)
d1, c_1, a, b = Polygon(A, B, C)
γ = Angle(A, C, B)
h = Segment(C, D)
i = Segment(D, E)
p = Segment(A, D)
q = Segment(D, B)
α = Angle(B, A, C)
β = Angle(D, C, B)
Vieleck1, f, j, k, l, F, G = Polygon(C, B, 4)
Vieleck2, m, n, r, s, H, I = Polygon(A, C, 4)
Vieleck3, t, d, e, f_1, J, K = Polygon(B, A, 4)
L, M = Intersect(g, Vieleck3)
v1, j_1, l_1, d_1, a_1 = Polygon(J, L, D, A)
v2, l_2, k_1, b_1, d_2 = Polygon(L, K, B, D)
e_1 = Circle(A, c)
g_1 = CircleArc(A, J, B)
N = (-10.216, 5.876)
O = (-8.516, 5.876)
Text1: "b^2=" + (LaTeX[b]) + "^2=" + (LaTeX[v1]) + ""
Text2: "p\cdot c=" + (LaTeX[v1]) + ""
Text3: "a^2=" + (LaTeX[a]) + "^2=" + (LaTeX[Vieleck1]) + ""
Text4: "q\cdot c=" + (LaTeX[v2]) + ""
Text5: "a^2+b^2=" + (LaTeX[a]) + "^2+" + (LaTeX[b]) + "^2"
Text6: "pc+qc=(p+q)c=c^2=" + (LaTeX[c]) + "^2
=" + (LaTeX[Vieleck3]) + ""
Text9: "=" + (LaTeX[v1]) + "+" + (LaTeX[v2]) + ""