Ipotesi\!:\ \overline{AB} \cong \overline{A'B'};\ 
\overline{AC} \cong \overline{A'C'};\ 
\overline{BC} \cong \overline{B'C'}\
Tesi\!:\ \triangle ABC \cong A'B'C'

1\ -\ \triangle ABC \cong A'B'C''\ -\ Per\ 
costruzione

2\ -\ \triangle A'C'C''\ è\ isoscele\ -\ 
\overline{AC'} \cong \overline{AC''}\ (Ip.); (1)\ e\ 
proprietà\ transitiva

3\ -\ A\^C'C'' \cong A\^C''C'\ -\ Teorema\!:\ 
angoli\ alla\ base\ triangolo\ isoscele

4\ -\ \triangle B'C'C''\ è\ isoscele\ -\ 
\overline{BC'} \cong \overline{BC''}\ (Ip.); (1)\ e\ 
proprietà\ transitiva

5\ -\ B\^C'C'' \cong B\^C''C'\ -\ Teorema\!:\ 
angoli\ alla\ base\ triangolo\ isoscele

6\ -\ A'\^C'B' \cong A'\^C''B'\ -\ 
Somma/Sottrazione\ di\ angoli\ congruenti

7\ -\ \triangle A'C'B' \cong A'C''B'\ -\ I\ criterio\!:\ 
\overline{A'C'} \cong \overline{A'C''}\ (2); 
\overline{B'C'} \cong \overline{B'C''}\ (4); 
A'\^C'B' \cong A'\^C''B'\ (6)

8\ -\ \triangle ABC \cong A'B'C'\ -\ Per\ (7)\ e\ 
proprietà\ transitiva\
Q.\ E.\ D.

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A = (0.9, 1.5)
B = (5.213818181818185, 1.516)
a = Segment(A, B)
C = (4.34, 4.06)
b = Segment(A, C)
c = Segment(B, C)
A' = (7.573818181818192, 1.50262)
B': (x(A') + x(B) - x(A), y(A') + y(B) - y(A))
d = Segment(A', B')
e = Circle(A', b)
f = Circle(B', c)
C' = Intersect(e, f, 1)
g = Segment(A', C')
h = Segment(C', B')
C'' = Intersect(e, f, 2)
i = Segment(C'', B')
j = Segment(C'', A')
k = Segment(C', C'')
α = Angle(A', C', C'')
α'' = Angle(C', C'', A')
β = Angle(C'', C', B')
β'' = Angle(B', C'', C')