Geometry for Elementary School/Copying a triangle

In this chapter, we will show how to copy a triangle $$\triangle ABC $$ to other triangle $$\triangle CDE $$. The construction is an excellent example of the reduction technique – solving a problem by solution to a previously solved problem.

The construction

 * 1) Construct a triangle from the sides of $$\triangle ABC $$ : $$\overline{AB}$$, $$\overline{AC}$$, $$\overline{BC}$$ and get $$\triangle CDE $$.

Claim
The triangles $$\triangle ABC $$ and $$\triangle CDE $$ are congruent.

Proof

 * 1) $$\overline{AB}$$, $$\overline{AC}$$, $$\overline{BC}$$ are sides of the  triangle  $$\triangle ABC $$ and therefore obey the triangle inequality.
 * 2) Therefore one can build a triangle whose sides equal these segments.
 * 3) The sides of the triangle $$\triangle ABC $$  and $$\triangle CDE $$ are equal.
 * 4) Due to ../The Side-Side-Side congruence theorem/ the triangles $$\triangle ABC$$ and $$\triangle CDE$$ congruence.

Geometria per scuola elementare/Copia di un triangolo