△PQR∼△JKL

Question

, which statements are correct?(1 point)
Responses

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

∠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¯¯¯¯¯¯¯
.

Answer 1

Given that triangles \( \triangle PQR \sim \triangle JKL \), it implies that the corresponding angles and sides of these triangles are proportional.

1. Corresponding Angles:

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

2. Corresponding Sides:

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

Now let's evaluate the statements provided:

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

   • Evaluation: Correct (angles are congruent and sides correspond).

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

   • Evaluation: Correct (angles are congruent and sides correspond).

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

   • Evaluation: Incorrect (angles do not correspond; \( \angle Q \) corresponds to \( \angle K \)).

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

   • Evaluation: Incorrect (sides do not correspond; \( \overline{PQ} \) corresponds to \( \overline{JK} \)).

Summary

• Correct Statements: 1 and 2
• Incorrect Statements: 3 and 4