Problem

For non-right triangles, evaluate evidence consisting of \(\text{two}~\text{corresponding}~\text{side}~\text{pairs}\) and a congruent non-included angle pair. State whether this \(SSA\) evidence guarantees congruence, similarity, \(\text{both}\), or neither, and explain the ambiguity.

Neutral evidence reference identifying two corresponding sides and a nonincluded angle in non-right triangles, without a conclusion about sufficiency.

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What this problem is really about

Evidence must be tested separately against the congruence and similarity criteria. We’ll classify the angle as non-included, examine the two-position ambiguity of SSA for non-right triangles, compare the data with every standard similarity test, and state only what the supplied information guarantees.

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SSA proves neither congruence nor similarity because the nonincluded angle can produce different triangles.

SSA proves only similarity because SAS does not require an included angle.

SSA proves congruence by AAA and proves similarity by AA.

SSA proves both congruence and similarity because it is equivalent to SAS.

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For non-right triangles, evaluate evidence consisting of \(\text{two}~\text{corresponding}~\text{side}~\text{pairs}\) and a congruent non-included angle pair. State whether this \(SSA\) evidence guarantees congruence, similarity, \(\text{both}\), or neither, and explain the ambiguity.

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