Question

If APQR ~ AJKL, which statements are correct? (1 point)

OZQZL and PQ corresponds to JK.

OZQZK and PR corresponds to JL.

OPLJ and QR corresponds to JK.

OPLJ and PQ corresponds to JL.

Answer 1

To determine which statements are correct given that triangles APQR and AJKL are similar (APQR ~ AJKL), we can use the properties of similar triangles. Similar triangles have corresponding sides that are proportional and corresponding angles that are equal.

In this similarity, the vertices correspond as follows based on the naming order:

- A corresponds to A
- P corresponds to J
- Q corresponds to K
- R corresponds to L

Now, let's analyze the statements:

1. **OZQZL and PQ corresponds to JK.**
- This statement is incorrect. Since P corresponds to J and Q corresponds to K, PQ corresponds to JK. OZQZL appears to have irrelevant points and does not align with the original correspondence.

2. **OZQZK and PR corresponds to JL.**
- This statement is incorrect. PR corresponds to JL. OZQZK again seems to feature irrelevant points and does not correspond properly.

3. **OPLJ and QR corresponds to JK.**
- This statement is incorrect. QR corresponds to KL, not JK.

4. **OPLJ and PQ corresponds to JL.**
- This statement is incorrect. PQ corresponds to JK, not JL.

In summary, none of the statements are correct based on the proportionality and correspondence of the sides of the similar triangles APQR and AJKL.