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¯¯¯¯¯¯¯
pick one

Answer 1

Given that triangles △PQR and △JKL are similar (△PQR ∼ △JKL), the corresponding angles and sides are proportional.

1. The angles of the triangles that are corresponding are:

   • ∠P ≅ ∠J
   • ∠Q ≅ ∠K
   • ∠R ≅ ∠L

2. The sides of the triangles that correspond are:

   • PQ corresponds to JK
   • QR corresponds to KL
   • PR corresponds to JL

Now, let's analyze each statement provided:

1. ∠P≅∠J and QR corresponds to JK - This statement is correct because ∠P corresponds to ∠J and QR does indeed correspond to JK.

2. ∠Q≅∠L and PQ corresponds to JK - This statement is incorrect as PQ corresponds to JK, but ∠Q corresponds to ∠K, not ∠L.

3. ∠Q≅∠K and PR corresponds to JL - This statement is correct as ∠Q does correspond to ∠K and PR corresponds to JL.

4. ∠P≅∠J and PQ corresponds to JL - This statement is incorrect as PQ corresponds to JK, not JL.

So, the correct statements are:

• Statement 1: ∠P≅∠J and QR corresponds to JK
• Statement 3: ∠Q≅∠K and PR corresponds to JL

Since you need to pick one, I would recommend choosing Statement 1 as it directly refers to the correlation of angles and sides between the two triangles.