# 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 ${\displaystyle \triangle ABC}$ to other triangle ${\displaystyle \triangle CDE}$ . 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 ${\displaystyle \triangle ABC}$  : ${\displaystyle {\overline {AB}}}$ , ${\displaystyle {\overline {AC}}}$ , ${\displaystyle {\overline {BC}}}$  and get ${\displaystyle \triangle CDE}$ .

## Claim

The triangles ${\displaystyle \triangle ABC}$  and ${\displaystyle \triangle CDE}$  are congruent.

## Proof

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