If △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≅∠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 .

∠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 .

∠P≅∠J
and PQ¯¯¯¯¯¯¯¯
corresponds to JL¯¯¯¯¯¯¯
.

Answer 1

When two triangles are similar, their corresponding angles are congruent and their corresponding sides are in proportion. Thus, given that \( \triangle PQR \sim \triangle JKL \), we can establish the following statements regarding their corresponding parts:

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

Now let's examine the statements you've provided:

1. Statement 1:

   • \( \angle P \cong \angle J \) and \( QR \) corresponds to \( JK \). (Correct)

2. Statement 2:

   • \( \angle Q \cong \angle L \) and \( PQ \) corresponds to \( JK \). (Incorrect), as \( PQ \) corresponds to \( JK \) should be with \( JK \).

3. Statement 3:

   • \( \angle Q \cong \angle K \) and \( PR \) corresponds to \( JL \). (Correct).

4. Statement 4:

   • \( \angle P \cong \angle J \) and \( PQ \) corresponds to \( JL \). (Incorrect), as \( PQ \) corresponds to \( JK \).

So, the correct statements are:

• Statement 1
• Statement 3.