Question

Question

If △PQR∼△JKL
△
P
Q
R
∼
△
J
K
L
, which statements are correct?(1 point)
Responses

∠Q≅∠L
∠
Q
≅
∠
L
and PQ¯¯¯¯¯¯¯¯
P
Q
¯
corresponds to JK¯¯¯¯¯¯¯¯
J
K
¯
.
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
∠
P
≅
∠
J
and PQ¯¯¯¯¯¯¯¯
P
Q
¯
corresponds to JL¯¯¯¯¯¯¯
J
L
¯
.
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 .

∠Q≅∠K
∠
Q
≅
∠
K
and PR¯¯¯¯¯¯¯¯
P
R
¯
corresponds to JL¯¯¯¯¯¯¯
J
L
¯
.
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
∠
P
≅
∠
J
and QR¯¯¯¯¯¯¯¯
Q
R
¯
corresponds to JK¯¯¯¯¯¯¯¯
J
K
¯
.

Answer 1

In similar triangles, corresponding angles are congruent, and the ratios of corresponding sides are equal. Given the notation that \( \triangle PQR \sim \triangle JKL \), we can determine the following correspondences:

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

Now let's evaluate each statement to see if it correctly describes the relationships based on the similarity of triangles.

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

   • This statement is incorrect. \( \angle Q \) corresponds to \( \angle K \), not \( \angle L \).

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

   • This statement is incorrect. \( \angle P \cong \angle J \) is true, but \( PQ \) corresponds to \( JK \), not \( JL \).

3. Statement: \( \angle Q \cong \angle K \) and \( PR \) corresponds to \( JL \).

   • This statement is incorrect. While \( \angle Q \cong \angle K \) is true, \( PR \) corresponds to \( JL \) is also incorrect because \( PR \) actually corresponds to \( KL \).

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

   • This statement is incorrect. While \( \angle P \cong \angle J \) is correct, \( QR \) corresponds to \( KL \), not \( JK \).

Based on these evaluations, none of the given statements are accurate descriptions of the relationships defined by triangle similarity \( \triangle PQR \sim \triangle JKL \).