Can a Triangle Be Divided Into 205 Congruent Triangles?

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SUMMARY

A triangle can indeed be divided into 205 congruent triangles. This conclusion is supported by geometric principles that allow for the subdivision of a triangle into smaller, equal-area triangles. The method involves using specific angles and side lengths to ensure that each of the 205 triangles maintains congruence. The proof leverages concepts from Euclidean geometry, particularly focusing on area preservation and congruence criteria.

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Prove that there exists a triangle which can be cut into 205 congruent
triangles.
 
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Albert said:
Prove that there exists a triangle which can be cut into 205 congruent
triangles.
hint:
Suppose that one side of a triangle has length $n$. Then it can be cut into $n^2$
congruent triangles which are similar to the original one and whose corresponding sides to
the side of length $n$ have lengths 1.
$205=a^2+b^2$ here $a,b\in N$
find all possible $a$ and $b$
 

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