11. If \( \triangle \mathrm{MNO} \cong \triangle \mathrm{PQR} \), which of the following can you NOT conclude as being true? \( \overline{\mathrm{NO}} \cong \overline{\mathrm{QR}} \) \( \angle \mathrm{M} \cong \angle \mathrm{P} \) \( \overline{\mathrm{MN}} \cong \overline{\mathrm{PR}} \) \( \begin{array}{l}\angle \mathrm{N} \cong \angle \mathrm{Q}\end{array} \)
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Beyond the Answer
If \( \triangle \mathrm{MNO} \cong \triangle \mathrm{PQR} \), it indicates that all corresponding sides and angles of both triangles are congruent. Therefore, you can confidently conclude statements about the relationships between the sides and angles. However, an incorrect statement might arise from misidentifying the correspondence, leading to an assumption that one side or angle corresponds to the wrong one in the other triangle—like asserting \( \overline{\mathrm{MN}} \cong \overline{\mathrm{QR}} \) when that isn't a correct correspondence. To avoid such errors, remember that congruence between triangles requires specific correspondences. Always double-check which sides and angles match up to prevent common mistakes. It’s like putting together a puzzle: you wouldn’t try to force the wrong piece in just because it looks similar!