Geometry for Elementary School/Copying a triangle

From Wikibooks, open books for an open world
< Geometry for Elementary School
Jump to: navigation, search
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[edit]

  1. Construct a triangle from the sides of \triangle ABC  : \overline{AB}, \overline{AC}, \overline{BC} and get \triangle CDE .

Claim[edit]

The triangles \triangle ABC and \triangle CDE are congruent.

Proof[edit]

  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.