Geometry for Elementary School/Copying a triangle

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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 a excellent example of the reduction technique – solving a problem by solution to a previously solved problem.

[edit] The construction

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

[edit] Claim

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

[edit] 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 The Side-Side-Side congruence theorem the triangles \triangle ABC and \triangle CDE congruence.
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