If △PQR is similar to △JKL (denoted as △PQR∼△JKL), it implies that the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are proportional.
According to the similarity of triangles:
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Angles in triangle PQR correspond to angles in triangle JKL in the following manner:
- ∠P corresponds to ∠J
- ∠Q corresponds to ∠K
- ∠R corresponds to ∠L
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Sides in triangle PQR correspond to sides in triangle JKL in the following manner:
- QR corresponds to JK
- PQ corresponds to JL
- PR corresponds to KL
Now, let's evaluate each statement:
A. ∠P≅∠J and QR corresponds to JK.
This statement is correct.
B. ∠Q≅∠L and PQ corresponds to JK.
This statement is NOT correct. (∠Q≅∠K, and PQ corresponds to JL)
C. ∠P≅∠J and PQ corresponds to JL.
This statement is NOT correct. (Again, ∠P≅∠J is correct, but PQ corresponds to JL is correct, making the entire statement incompatible.)
D. ∠Q≅∠K and PR corresponds to JL.
This statement is NOT correct. (∠Q≅∠K is correct, but PR corresponds to KL, not JL.)
In conclusion: The only correct statement is statement A.