Geometry for Elementary School/Copying a triangle
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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]
- Construct a triangle from the sides of : , , and get .
Claim[edit | edit source]
The triangles and are congruent.
Proof[edit | edit source]
- , , 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.