Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.
Solve algebraic congruence data before applying a criterion
Problem
Use this algebraic congruence information to solve for the variable and name the congruence criterion: \(AB=2x+3\), \(DE=11\), \(BC=7\), \(EF=7\), and included angles \(B\) and \(E\) are congruent.
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What this problem is really about
Separate the algebra from the geometry. First equate the expressions attached to corresponding sides and solve that equation, then substitute back to verify the lengths really match; only after that new congruence fact is established should you combine it with the remaining side and included-angle information to classify the triangle evidence.
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