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

The construction[edit | edit source]

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

Claim[edit | edit source]

The triangles and are congruent.

Proof[edit | edit source]

  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.