Geometry for Elementary School/Copying an angle

In this chapter, we will show how to copy an angle $$\angle ABC$$ to other angle $$\angle CDE$$. The construction is based on Book I, proposition 23.

The construction

 * 1)  Draw a line between A and C and get $$\triangle ABC$$.
 * 2) Copy the triangle $$\triangle ABC$$ and get $$\triangle CDE$$

Claim
The angles $$\angle ABC$$ and $$\angle CDE$$ are equal.

Proof

 * 1) The triangles $$\triangle ABC$$ and $$\triangle CDE$$ congruence.
 * 2) Therefore the angles of the triangles equal.
 * 3) Hence, $$\angle ABC$$  and $$\angle CDE$$ are equal.

Note that any two points on the rays can be used to create a triangle.

Geometria per scuola elementare/Copiare un angolo