Ipotesi\!:\ \alpha \cong \beta\
Tesi\!: \alpha \cong \delta;\ \alpha + \gamma =
 \pi;\ \varphi \cong \gamma\ ...

1\ -\ \beta \cong \delta\ -\ Opposti\ al\ vertice

2\ -\ \alpha \cong \delta\ -\ Per\ (1)\ e\ (Ip.)\ -\ 
Prima\ parte\ tesi

3\ -\ \delta + \gamma = \pi\ -\ Per\ costruzione

4\ -\ \alpha + \gamma = \pi\ -\ Per\ (3)\ e\ (Ip.)\ -\ 
Seconda\ parte\ tesi

5\ -\ \gamma \cong \epsilon\ -\ Opposti\ al\ 
vertice

6\ -\ \alpha + \varphi = \pi\ -\ Per\ costruzione

7\ -\ \varphi \cong \gamma\ - \ Per\ (4);\ 
(5)\ e\ (6)\
Q.\ E.\ D.

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A = (4.84, 3.7)
B = (8.36, 3.7)
r = Line(A, B)
C = (7.5, 1.98)
α = Angle(A, B, C)
B' = Rotate(B, (-α), C)
β = Angle(B', C, B)
s = Line(C, B')
t = Line(B, C)
γ = Angle(B, C, Point[s])
δ = Angle(Point[s], C, Point[t])
D = Rotate(Point[t], γ, C)
ε = Angle(Point[t], C, D)
E = Rotate(Point[r], (-γ), B)
φ = Angle(Point[r], B, E)