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If △PQR∼△JKL

, which statements are correct?(1 point)
Responses

∠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 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¯¯¯¯¯¯¯
.

1 answer

Given that triangles \(\triangle PQR \sim \triangle JKL\), we can conclude that corresponding angles are congruent and corresponding sides are in proportion.

The correct statements based on the properties of similar triangles are:

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

Corresponding sides will also match as follows:

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

Let’s evaluate the given options:

  1. ∠Q≅∠L and PQ corresponds to JK.

    • This is incorrect. \(\angle Q\) corresponds with \(\angle K\) (not \(\angle L\)), and \(PQ\) corresponds to \(JK\), which is correct.
    • Overall this is partially correct.

  2. ∠P≅∠J and QR corresponds to JK.

    • This is incorrect because \(\angle P\) does indeed correspond to \(\angle J\), but \(QR\) corresponds with \(KL\), not \(JK\).
    • Thus, this is incorrect.

  3. ∠P≅∠J and PQ corresponds to JL.

    • This is incorrect because while \(\angle P\) corresponds to \(\angle J\), \(PQ\) corresponds to \(JK\) not \(JL\).
    • Thus, this is incorrect.

  4. ∠Q≅∠K and PR corresponds to JL.

    • This is incorrect because \(\angle Q\) does correspond to \(\angle K\) but \(PR\) corresponds to \(JL\), which is incorrect as well. PR actually corresponds to KL.
    • Thus, this is incorrect.

The only statement that is partially correct is the first option regarding angles and side correspondence, but it makes a mistake regarding the angles. Therefore, careful review is needed; review which pairs of angles correspond correctly:

  • \(\angle Q \cong \angle K\)
  • \(\angle P \cong \angle J\)
  • The side correspondences are essential to get the correct conclusions.

Final Conclusion:

The correct statements regarding the angles and lines will reflect correct angle to angle correspondence and side to side correspondence. The analysis here shows the deeper need to connect angles and sides correctly in similarity statements.

For answering your query: Check your angle and side pairings for correctness as outlined above to clarify where your statements can be true as a whole.