Concept guide
Congruence: deciding congruence of labeled triangles by the SSS slice
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.