Ipotesi\!: \overline{AC} \cong \overline{BC}

Tesi\!: \alpha \cong \alpha'

1\ -\ \beta \cong \beta'\ -\ Per\ costruzione\ di\ 
\overline{CE}\ bisettrice\ di\ A\^CB

2\ -\ \triangle ACE \cong BCE\ -\ I\ criterio\!:\ 
\overline{CE}\ comune;\ 
\overline{AC} \cong \overline{BC}\ (Ip.);\ 
\beta \cong \beta'\ (1)

3\ -\ \alpha \cong \alpha'\ -\ Angoli\ 
corrispondenti\ di\ triangoli\ congruenti\ (2)\
Q.\ E.\ D.

http://www.profcortese.net

A = (2.92, -0.44)
B = (6.56, -0.46)
a = Segment(A, B)
P:(3.26, 3.36)
c = Circle(B, P)
d = Circle(A, Distance[B, P])
C = Intersect(c, d, 2)
b = Segment(B, C)
e = Segment(C, A)
α = Angle(B, A, C)
α' = Angle(C, B, A)
A' = Rotate(A, 90° - α, C)
β = Angle(A, C, A')
f = Line(C, A')
E = Intersect(f, a)
g = Segment(C, E)
β' = Angle(E, C, B)

Tool: Provatriangolo7
Provatriangolo7[ <Punto>, <Punto>, <Punto> ]
Input: A, B, C
Output: poli1

c = Circle(B, C)
b = Segment(B, C)
d = Circle(A, b)
D = Intersect(c, d, 2)
poli1, d_1, a_1, b_1 = Polygon(A, B, D)

Tool: ProvaTriangolo9
Input: A, B, C
Output: a, poli1

a = Segment(A, B)
b = OrthogonalLine(C, a)
D = Intersect(b, a)
c = Segment(C, D)
d = LineBisector(a)
E = Intersect(d, a)
e = Circle(E, c)
F = Intersect(e, d, 2)
poli1, f, a_1, b_1 = Polygon(A, B, F)

Tool: ProvaTriangolo10
Input: A, B, C
Output: poli1, F

a = Segment(A, B)
b = OrthogonalLine(C, a)
D = Intersect(b, a)
c = Segment(C, D)
d = LineBisector(a)
E = Intersect(d, a)
e = Circle(E, c)
F = Intersect(e, d, 2)
poli1, f, a_1, b_1 = Polygon(A, B, F)