# Geometry for Elementary School/Copying a triangle

 Geometry for Elementary School Copying a line segment Copying a triangle Copying an angle

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.