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If △PQR∼△JKL

Which statements are correct? (1 point)

∠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¯¯¯¯¯¯¯
.
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 .

1 answer

Given that \( \triangle PQR \sim \triangle JKL \), we know that corresponding angles are equal, and the lengths of corresponding sides are in proportion.

From this similarity, we can determine the following correspondences:

  1. \( \angle P \equiv \angle J \)
  2. \( \angle Q \equiv \angle K \)
  3. \( \angle R \equiv \angle L \)

And the sides correspond as follows:

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

Now, let’s evaluate each statement:

  1. Statement 1:

    • \( \angle P \equiv \angle J \)
    • \( QR \) corresponds to \( JK \)
    • This statement is correct because it accurately reflects the correspondence of angles and sides.

  2. Statement 2:

    • \( \angle Q \equiv \angle L \)
    • \( PQ \) corresponds to \( JK \)
    • This statement is incorrect because \( PQ \) actually corresponds to \( JK \) not \( PQ \).

  3. Statement 3:

    • \( \angle P \equiv \angle J \)
    • \( PQ \) corresponds to \( JL \)
    • This statement is incorrect because \( PQ \) should correspond to \( JK \).

  4. Statement 4:

    • \( \angle Q \equiv \angle K \)
    • \( PR \) corresponds to \( JL \)
    • This statement is incorrect because \( PR \) corresponds to \( JL \) but not \( K \).

Given the analysis, the only correct statement is Statement 1.