If △PQR∼△JKL

Question

, which statements are correct?(1 point)
Responses

∠Q≅∠L
and PQ¯¯¯¯¯¯¯¯
corresponds to JK¯¯¯¯¯¯¯¯
.
angle upper Q congruent to angle upper L and Modifying above upper P upper Q with bar corresponds to Modifying above upper J upper K with bar .

∠P≅∠J
and PQ¯¯¯¯¯¯¯¯
corresponds to JL¯¯¯¯¯¯¯
.
angle upper P congruent to angle upper J and Modifying above upper P upper Q with bar corresponds to Modifying above upper J upper L with bar .

∠P≅∠J
and QR¯¯¯¯¯¯¯¯
corresponds to JK¯¯¯¯¯¯¯¯
.
angle upper P congruent to angle upper J and Modifying above upper Q upper R with bar corresponds to Modifying above upper J upper K with bar .

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

Answer 1

Given that \( \triangle PQR \sim \triangle JKL \), we can conclude that the corresponding angles are congruent and the corresponding sides are in proportion.

1. The corresponding angles are as follows:

   • \( \angle P \) corresponds to \( \angle J \)
   • \( \angle Q \) corresponds to \( \angle K \)
   • \( \angle R \) corresponds to \( \angle L \)

2. The corresponding sides are:

   • \( PQ \) corresponds to \( JK \)
   • \( QR \) corresponds to \( KL \)
   • \( PR \) corresponds to \( JL \)

Thus, let's evaluate each statement:

1. Statement: \( \angle Q \cong \angle L \) and \( \overline{PQ} \) corresponds to \( \overline{JK} \).

   • Evaluation: Incorrect. \( \angle Q \) corresponds to \( \angle K \), not \( \angle L \).

2. Statement: \( \angle P \cong \angle J \) and \( \overline{PQ} \) corresponds to \( \overline{JL} \).

   • Evaluation: Incorrect. While \( \angle P \) does correspond to \( \angle J \), \( \overline{PQ} \) corresponds to \( \overline{JK} \), not \( \overline{JL} \).

3. Statement: \( \angle P \cong \angle J \) and \( \overline{QR} \) corresponds to \( \overline{JK} \).

   • Evaluation: Incorrect. While \( \angle P \cong \angle J \) is correct, \( \overline{QR} \) corresponds to \( \overline{KL} \).

4. Statement: \( \angle Q \cong \angle K \) and \( \overline{PR} \) corresponds to \( \overline{JL} \).

   • Evaluation: Correct. \( \angle Q \cong \angle K \) is true, and \( \overline{PR} \) corresponds to \( \overline{JL} \).

Therefore, the correct statement is:

∠Q ≅ ∠K and PR corresponds to JL.