Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.
Detect the first invalid claim in a triangle congruence proof
Problem
Here are the proof claims, in order: \(AB=DE\) given, \(BC=EF\) given, \(\angle~A=\angle~D\) given, \(\triangle~ABC~\cong~\triangle~DEF\) by \(SAS\). Identify the first invalid claim.
Audit the proof chronologically and distinguish an unhelpful given from an unsupported deduction: a stated premise may be true without proving the desired result. At the first derived claim, compare its theorem’s exact requirements with the supplied parts, especially whether the angle occupies the required position between the two sides.
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