# Concept derivation guides

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Concept guide



## [Congruence: deciding congruence of labeled triangles by the SSS slice](/en/derivations/derivation-mko-congruence-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-congruence)

In one equal-unit orthonormal plane, let A1=(0,0), A2=(4,0), A3=(0,3) and B1=(1,1), B2=(1,5), B3=(4,1), with explicit correspondence Ai↔Bi. First verify by determinants that both triples are nondegenerate triangles, then compare squared side lengths exactly in the order 12, 13, 23 to decide G(A,B); explain why B has the opposite orientation and is still congruent; finally find the first unequal witness for the other correspondence A1↔B1, A2↔B3, A3↔B2, and show that a degenerate triple is not eligible.

Congruence of nondegenerate triangles with explicit correspondence

derivation-mko-congruence-01





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