Use rigid motions to transform figures and decide whether two figures are congruent.
Reject congruence using a specific measurement mismatch
Problem
Explain why a triangle with side lengths \(5\), \(5\), \(8\) is not congruent to a triangle with side lengths \(5\), \(6\), \(8\), using the specific measurement mismatch.
To test congruence from side data, sort each triangle’s complete length list and compare corresponding entries. Two matching lengths do not rescue a failed third pair: one unequal measurement is enough because every rigid motion preserves every side length.
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