If △PQR∼△JKL, which statements are correct?

A. ∠P≅∠J and
QR

corresponds to
JK
. B. ∠Q≅∠L and
PQ

corresponds to
JK
. C. ∠P≅∠J and
PQ

corresponds to
JL
. D. ∠Q≅∠K and
PR
corresponds to
JL

1 answer

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:

  • 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
  • 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.