«قضیه تالس»

}

⇒

\frac{AD}{DB}=\frac{AE}{EC}

«تعمیم قضیه تالس»

}

⇒

\frac{AD}{AB}=\frac{AE}{AC}

A = (-4.071491442417764, 6.435348097978444)
B = (-7.6441913147128115, -14.766575734329864)
C = (2.253944397055436, -14.825144584695357)
poly1, c, a, b = Polygon(A, B, C)
D = Point(c)
d = Line(D, a)
E = Intersect(d, b)
e = Segment(E, D)
f = Segment(A, D)
g = Segment(A, E)
h = Segment(E, C)
i = Segment(D, B)
m: f / i
text2: "\frac{AD}{DB}=\frac{" + (LaTeX[f]) + "}{" + (LaTeX[i]) + "}=" + (LaTeX[m]) + ""
text3: "\frac{AE}{EC}=\frac{" + (LaTeX[g]) + "}{" + (LaTeX[h]) + "}=" + (LaTeX[m]) + ""
α: g / h
n: g / b
text8: "\frac{AD}{AB}=\frac{" + (LaTeX[f]) + "}{" + (LaTeX[c]) + "}=" + (LaTeX[n]) + ""
text9: "\frac{AE}{AC}=\frac{" + (LaTeX[g]) + "}{" + (LaTeX[b]) + "}=" + (LaTeX[n]) + ""