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 analyze the possible correspondences between the triangles' angles.
Typically, when two triangles are congruent, their corresponding angles are also congruent. Without specific details on the mapping chosen for the two triangles, we can assess the options:
- Option #1: ∠L≅∠D
- Option #2: ∠K≅∠E
- Option #3: ∠J≅∠D
- Option #4: ∠L≅∠F
To identify the incorrect pair, we should note that if angles in these two triangles are supposed to correspond under a congruence mapping, the angles matched should indeed be congruent.
Assuming a standard assignment, if we let:
- ∠J correspond to ∠D
- ∠K correspond to ∠E
- ∠L correspond to ∠F
Then options would be congruent:
- ∠J should correspond to ∠D (Option #3 has an issue if this holds),
- ∠K should correspond to ∠E (Option #2 is fine),
- ∠L should correspond to ∠F (Option #4 is fine),
Looking at Option #3, if ∠J is matched with ∠D but is angles are actually corresponding to others based on congruency statement, this leads to potential incongruence.
So, if we examine: Option #3: ∠J≅∠D is most likely the contradiction under the assumptions.
This suggests Option #3 shows a pair of angles that are not congruent when mapping \( \triangle JKL \) onto \( \triangle DEF \).
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