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Geometry for Elementary School/Copying a triangle
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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
Construct a triangle from the sides of : , , and get .
Claim
The triangles and are congruent.
Proof
, , are sides of the triangle and therefore obey the triangle inequality.
Therefore one can build a triangle whose sides equal these segments.
The sides of the triangle and are equal.
Due to ../The Side-Side-Side congruence theorem/ the triangles and congruence.
it:Geometria per scuola elementare/Copia di un triangolo