To determine which option shows a pair of angles that are not congruent when mapping triangle \( \triangle JKL \) onto triangle \( \triangle DEF \), we need to understand how the angles correspond based on their positions in the triangles.
- Generally, when two triangles are congruent, their corresponding angles are congruent.
- When mapping \( \triangle JKL \) onto \( \triangle DEF \), we typically have:
- \( \angle J \) corresponding to \( \angle D \)
- \( \angle K \) corresponding to \( \angle E \)
- \( \angle L \) corresponding to \( \angle F \)
Given this correspondence, we can analyze the options for any pairs that would not be congruent:
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Option #1: \( \angle L \cong \angle D \) (congruent if mapped correctly)
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Option #2: \( \angle K \cong \angle E \) (congruent if mapped correctly)
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Option #3: \( \angle J \cong \angle D \) (not a valid match, since \( J \) should correspond to \( D \), but if they are misaligned, we assume not congruent)
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Option #4: \( \angle L \cong \angle F \) (congruent if mapped correctly)
Based on the logical correspondence established in angles, Option #3 indicates a potential mismatch if \( \angle J \) is not aligned correctly with \( D \). Therefore:
Option #3: \( \angle J \cong \angle D \) shows a pair of angles that are not congruent if they are misaligned.
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