Ipotesi\!: \overline{AB} \cong \overline{A'B'};\ 
C\^AB \cong C'\^A'B';\ C\^BA \cong C'\^B'A'

Tesi\!: \triangle ABC \cong \triangle A'B'C'

1\ -\ Supponiamo\ \overline{AC} \not\cong
 \overline{A'C'}\ -\ Ipotesi\ aggiuntiva\ da\ confutare

2\ -\ \exists D \in \overline{AC}\ tale\ che\ 
\overline{AD} \cong \overline{A'C'}\ -\ Per\ (1)\ 
(nota\!:\ se\ \overline{A'C'} > \overline{AC}\ 
si\ invertono\ i\ ruoli)

3\ -\ \triangle ABD \cong \triangle A'B'C'\ -\ I\ criterio\!:\ 
\overline{AD} \cong \overline{A'C'}\ (2);\ 
D\^AB \cong C'\^A'B'\ (Ip.);\ \overline{AB} \cong \overline{A'B'}\ 
(Ip.)

4\ -\ A\^BD \cong A'\^B'C' \cong A\^BC\ -\ Per\ (4)\ e\ Ip.

5\ -\ A\^BD \cong A\^BC\ -\ Proprietà\ transitiva\ -\ 
Affermazione\ falsa\ perchè\ D\ è\ interno\ a\ A\^BC

6\ -\ \overline{AC} \cong \overline{A'C'}\ -\ 
(5)\ è\ falsa\ per\ cui\ (1)\ è\ necessariamente\ falsa

7\ -\ \triangle ABC \cong \triangle A'B'C'\ -\ I\ criterio\!:\ 
\overline{AC} \cong \overline{A'C'}\ (6);\ 
D\^AB \cong C'\^A'B'\ (Ip.);\ \overline{AB} \cong \overline{A'B'}\ 
(Ip.)
\
Q.\ E.\ D.

http://www.profcortese.net

A = (1.6, 0.76)
B = (6.06, 0.76)
C = (3.02, 4.82)
poli1, c, a, b = Polygon(A, B, C)
α = Angle(B, A, C)
β = Angle(C, B, A)
A' = (8.9, 0.74)
B': (x(A') + x(B) - x(A), y(A') + y(B) - y(A))
d = Segment(A', B')
B'' = Rotate(B', α, A')
α' = Angle(B', A', B'')
e = Line(A', B'')
A'' = Rotate(A', (-β), B')
β' = Angle(A'', B', A')
f = Line(B', A'')
C' = Intersect(e, f)
g = Segment(A', C')
h = Segment(B', C')
D = Point(b)
i = Segment(B, D)

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)