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.