Problem

\(\text{Three}~\text{corresponding}~\text{side}~\text{pairs}\) in \(\text{two}~\text{triangles}\) are congruent, with \(\text{no}~\angle~\text{information}\) supplied. Name the congruence criterion this evidence satisfies and justify the match.

Unworked triangle geometry showing exactly the supplied side, angle, scale, or context evidence.

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What this problem is really about

A valid congruence criterion must match exactly the evidence supplied. We’ll inventory the three marked side pairs, note that no angle relationship is available, recover the vertex mapping from the side endpoints, and state the congruence relationship in that consistent order.

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The criterion is AAS because once corresponding parts match, two angles and a side are enough to conclude congruence.

The criterion is SSS because the evidence gives three corresponding pairs of congruent sides and no angle information is needed.

The criterion is ASA because congruence tests usually depend on angle information along with one matching side.

The criterion is SAS because the evidence gives side congruence, so one angle is understood to go with the sides.

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\(\text{Three}~\text{corresponding}~\text{side}~\text{pairs}\) in \(\text{two}~\text{triangles}\) are congruent, with \(\text{no}~\angle~\text{information}\) supplied. Name the congruence criterion this evidence satisfies and justify the match.

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