Problem

Based on these measures, are the \(\text{two}\) triangles congruent, not congruent, or is there not enough information: triangle \(ABC\) has sides \(3,4,5\) and triangle \(DEF\) has sides \(3,4,5\)?

Triangle or coordinate diagram presenting only the geometric data supplied in the prompt.

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What this problem is really about

Complete side data can settle triangle congruence without separately measuring angles. Order both side-length lists, pair equal lengths consistently, and ask whether all three pairs match; position or reflected orientation is irrelevant because rigid motions can change either without changing the triangle’s measurements.

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The triangles are not congruent because the side lengths are only listed in a different triangle name, so the matching order is unclear.

The triangles are congruent because both have side lengths 3, 4, and 5, so all three corresponding sides can match.

There is not enough information because triangles with the same side lengths could still be different shapes when turned or flipped.

There is not enough information because side lengths alone do not tell whether two triangles have the same angles.

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Based on these measures, are the \(\text{two}\) triangles congruent, not congruent, or is there not enough information: triangle \(ABC\) has sides \(3,4,5\) and triangle \(DEF\) has sides \(3,4,5\)?

What this problem is really about

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