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 to other triangle . The construction is an excellent example of the reduction technique – solving a problem by solution to a previously solved problem.

The constructionEdit

  1. Construct a triangle from the sides of   :  ,  ,   and get  .

ClaimEdit

The triangles   and   are congruent.

ProofEdit

  1.  ,  ,   are sides of the triangle   and therefore obey the triangle inequality.
  2. Therefore one can build a triangle whose sides equal these segments.
  3. The sides of the triangle   and   are equal.
  4. Due to The Side-Side-Side congruence theorem the triangles   and   congruence.