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If △PQR∼△JKL

, 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 .

∠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¯¯¯¯¯¯¯
.

1 answer

When two triangles are similar (denoted as \( \triangle PQR \sim \triangle JKL \)), it implies that their corresponding angles are congruent and the lengths of corresponding sides are proportional.

From the given information, we can deduce 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 \( QR \) corresponds to side \( KL \)
    • Side \( PQ \) corresponds to side \( JK \)
    • Side \( PR \) corresponds to side \( JL \)

Now, let’s assess each statement based on the correspondences established above:

  1. Statement Analysis:

    • Statement 1: \( \angle P \cong \angle J \) and \( QR \) corresponds to \( JK \).

      • This is incorrect because \( QR \) should correspond to \( KL \).

    • Statement 2: \( \angle Q \cong \angle L \) and \( PQ \) corresponds to \( JK \).

      • This is incorrect as well; \( PQ \) actually corresponds to \( JK \), but \( \angle Q \) corresponds to \( \angle K \), not \( \angle L \).

    • Statement 3: \( \angle P \cong \angle J \) and \( PQ \) corresponds to \( JL \).

      • This is incorrect because \( PQ \) corresponds to \( JK \), not \( JL \).

    • Statement 4: \( \angle Q \cong \angle K \) and \( PR \) corresponds to \( JL \).

      • This is incorrect since \( PR \) should correspond to \( JL \), but it does mention a correct angle relationship; however, the side correspondence is incorrect.

Conclusion: None of the statements are completely correct. Each statement contains at least one incorrect correspondence related to sides or angles.