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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 .

∠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 .

∠Q≅∠L
and PQ¯¯¯¯¯¯¯¯
corresponds to JK¯¯¯¯¯¯¯¯
.

1 answer

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

From the similarity of the triangles, we can deduce the following:

  1. Corresponding angles:

    • \( \angle P \equiv \angle J \)
    • \( \angle Q \equiv \angle K \)
    • \( \angle R \equiv \angle L \)

  2. Corresponding sides:

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

Now let's analyze the provided statements:

  1. Statement 1:

    • \( \angle P \equiv \angle J \)
    • \( QR \) corresponds to \( JK \)
    • Correct: The angle relationship is correct, but the side correspondence is incorrect; \( QR \) should correspond to \( JL \).

  2. Statement 2:

    • \( \angle P \equiv \angle J \)
    • \( PQ \) corresponds to \( JL \)
    • Incorrect: The angle relationship is correct, but the side correspondence is incorrect; \( PQ \) should correspond to \( JK \).

  3. Statement 3:

    • \( \angle Q \equiv \angle K \)
    • \( PR \) corresponds to \( JL \)
    • Incorrect: The angle relationship is correct, but the side correspondence is incorrect; \( PR \) should correspond to \( KL \).

  4. Statement 4:

    • \( \angle Q \equiv \angle L \)
    • \( PQ \) corresponds to \( JK \)
    • Incorrect: The angle relationship is incorrect; \( \angle Q \) corresponds to \( \angle K \), not \( \angle L \).

Based on this analysis, the only part that is entirely correct is that the first portion of Statement 1 is correct about angle relationships, but the side correspondence is wrong. Similarly for Statement 2 and Statement 3; only the angle relationships are correct, while the side correspondences are wrong.

Therefore, none of the statements are fully correct. However, Statement 1 is partially correct in terms of angle correspondence.