If △PQR∼△JKL

Question

, which statements are correct?(1 point)
Responses

∠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 .

∠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 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¯¯¯¯¯¯¯¯
.

Answer 1

In similar triangles △PQR and △JKL, the corresponding angles and sides are proportional. Here’s what we know:

• Corresponding angles:

  • ∠P corresponds to ∠J
  • ∠Q corresponds to ∠K
  • ∠R corresponds to ∠L

• Corresponding sides:

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

Now, let’s analyze the given statements:

1. ∠P ≅ ∠J and PQ corresponds to JL

   • This statement is incorrect because it incorrectly states that the side PQ corresponds to JL. It should correspond to JK.

2. ∠Q ≅ ∠K and PR corresponds to JL

   • This statement is incorrect because PR corresponds to JL, but ∠Q ≅ ∠K is true.

3. ∠P ≅ ∠J and QR corresponds to JK

   • This statement is incorrect as well because QR corresponds to KL, not JK.

4. ∠Q ≅ ∠L and PQ corresponds to JK

   • This statement is incorrect because ∠Q ≅ ∠K, not ∠L.

Given this analysis, none of the statements match the correct relationships between the angles and sides of the triangles. The key points to remember are:

• ∠P ≅ ∠J and PQ corresponds to JK
• ∠Q ≅ ∠K and QR corresponds to KL
• ∠R ≅ ∠L and PR corresponds to JL

If any mistakes are present in the answers above, please clarify, and I'll help correct them!