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Question

If △PQR∼△JKL
, 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 .

∠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≅∠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 .

1 answer

Since △PQR is similar to △JKL (noted as △PQR∼△JKL), it implies that corresponding angles are equal and corresponding sides are proportional.

Given this, the correct pairs would be:

  1. Corresponding Angles:

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

  2. Corresponding Sides:

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

Now, let's evaluate the statements based on these facts:

  1. Statement 1:

    • ∠P≅∠J
    • PQ corresponds to JL. (Incorrect; should correspond to JK)

  2. Statement 2:

    • ∠P≅∠J
    • QR corresponds to JK. (Incorrect; QR should correspond to KL)

  3. Statement 3:

    • ∠Q≅∠K
    • PR corresponds to JL. (Incorrect; PR should correspond to JL)

  4. Statement 4:

    • ∠Q≅∠L
    • PQ corresponds to JK. (Incorrect; ∠Q corresponds to ∠K, and PQ corresponds to JK)

Based on this analysis, none of the provided statements are completely correct. The accurate statements should affirm the following pairs:

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

Consider revisiting the statements to see if a clearer set of definitions can be made.