Ipotesi\!:\ \overline{AB} \cong \overline{A'B'},\ 
\overline{AC} \cong \overline{A'C'},\ 
B\^AC>B'\^A'C'

Tesi\!:\ \overline{BC}>\overline{B'C'}

1\ -\ B\hat{A}D \cong B'\hat{A'}C'\ -\ Per\ costruzione

2\ -\ \overline{AD} \cong \overline{AC} 
\cong  \overline{A'C'}\ -\ 
Per\ costruzione

3\ -\ \triangle ABD \cong \triangle A'B'C'\ -\ 
I\ crit.\!:\ \overline{AB} \cong 
\overline{A'B'}\ (Ip.);\ 
\overline{BD} \cong \overline{B'C'}\ (2);\ 
B\hat{A}D \cong B'\hat{A'}C'\ (1)

4\ -\ \overline{BD} \cong \overline{B'C'}\ -\ Per\ (3)

5\ -\ D\hat{A}E \cong E'\hat{A}C\ -\ 
\overline{AE}\ bisettrice\ per\ costruzione

6\ -\ \triangle AED \cong \triangle AEC\ -\ 
I\ criterio\!:\ \overline{AD} \cong 
\overline{AC}\ (2);\ 
\overline{AE}\ comune;\ 
D\hat{A}E \cong E'\hat{A}C\ (5)

7\ -\ \overline{ED} \cong \overline{EC}\ -
\ Per\ (6)

8\ -\ \overline{BE}+\overline{ED}=\overline{BC}\ -
\ Per\ (7)

9\ -\ \overline{BE}+\overline{ED}>\overline{BD}\ -
\ Disuguaglianza\ triangolare

10\ -\ \overline{BC}>\overline{B'C'}\ -
\ Proprietà\ transitiva\ su\ (4),\ (8),\ (9)
\Q.\ E.\ D.

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B = (-2.26, 0.86)
C = (3.1, 0.86)
A = (1.04, 3.54)
poli1, c, a, b = Polygon(B, C, A)
α = Angle(B, A, C)
A' = (1.04, -0.5)
B' = Point(Circle[A', b])
d = Segment(A', B')
β = 0.7714355293814937 rad (slider from ° to α - °, step 0.1°)
B'' = Rotate(B', β, A')
γ = Angle(B', A', B'')
f = Ray(A', B'')
C' = Intersect(Circle[A', a], f)
e = Segment(A', C')
g = Segment(B', C')
P = Rotate(B, β, A)
δ = Angle(B, A, P)
D = Intersect(Circle[A, a], Ray[A, P])
h = Segment(A, D)
i = Segment(B, D)
E = Intersect(c, AngularBisector[D, A, C])
j = Segment(A, E)
k = Segment(D, E)