If △PQR∼△JKL

Question

, which statements are correct?(1 point)
Responses

∠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¯¯¯¯¯¯¯
.
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¯¯¯¯¯¯¯¯
.

Answer 1

Since \( \triangle PQR \sim \triangle JKL \) indicates that the two triangles are similar, we can use the properties of similar triangles to determine which statements are correct.

For similar triangles:

• Corresponding angles are congruent.
• Corresponding sides are in proportion.

Based on the similarity \( \triangle PQR \sim \triangle JKL \):

1. Angles:

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

2. Sides:

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

Based on this information, we can analyze the statements provided:

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

   • Correct (both expressions are true).

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

   • Incorrect (only the first part is incorrect, \( \angle Q \) corresponds to \( \angle K \)).

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

   • Incorrect (the second part is incorrect, \( \overline{PQ} \) corresponds to \( \overline{JK} \)).

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

   • Incorrect (the second part is incorrect, \( \overline{QR} \) corresponds to \( \overline{KL} \)).

Conclusion: The first statement is correct.