Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.
Evaluate which congruence criterion is valid and efficient
Problem
For triangles \(ABC\) and \(DEF\) with \(A\leftrightarrow~D\), \(B\leftrightarrow~E\), \(C\leftrightarrow~F\), the marked facts are \(AB\cong~DE\), \(BC\cong~EF\), \(AC\cong~DF\), and \(\angle~B\cong~\angle~E\). Determine every valid congruence criterion formed from exactly \(\text{three}\) marked facts and state each fact set.
Because the task asks for every valid three-fact set, treat it as an exhaustive inventory rather than a search for one convenient proof. Omit each marked fact in turn, classify the three that remain, and test both the part types and any included placement against the exact requirements of the standard congruence criteria.
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