If △PQR∼△JKL , which statements are correct?(1 point)

Question

∠P≅∠J and PQ¯¯¯¯¯¯¯¯ corresponds to JL¯¯¯¯¯¯¯ .
∠P≅∠J and QR¯¯¯¯¯¯¯¯ corresponds to JK¯¯¯¯¯¯¯¯ . 
∠Q≅∠L and PQ¯¯¯¯¯¯¯¯ corresponds to JK¯¯¯¯¯¯¯¯ .
∠Q≅∠K and PR¯¯¯¯¯¯¯¯ corresponds to JL¯¯¯¯¯¯¯ .

GPT-4o mini · Answer

If the triangles $ \Delta PQR \sim \Delta JKL $ (meaning they are similar), then the following statements are true about their corresponding angles and sides: 1. **Corresponding Angles**: - $ \angle P \cong \angle J $ - $ \angle Q \cong \angle K $ - $ \angle R \cong \angle L $ 2. **Corresponding Sides**: - $ PQ $ corresponds to $ JK $ - $ QR $ corresponds to $ KL $ - $ PR $ corresponds to $ JL $ Now let’s evaluate the statements one by one: 1. **Statement**: $ \angle P \cong \angle J $ and $ PQ $ corresponds to $ JL $. - This statement is **incorrect** because $ PQ $ corresponds to $ JK $, not $ JL $. 2. **Statement**: $ \angle P \cong \angle J $ and $ QR $ corresponds to $ JK $. - This statement is **incorrect** because $ QR $ actually corresponds to $ KL $, not $ JK $. 3. **Statement**: $ \angle Q \cong \angle L $ and $ PQ $ corresponds to $ JK $. - This statement is **incorrect** because $ \angle Q $ actually corresponds to $ \angle K $, not $ \angle L $. 4. **Statement**: $ \angle Q \cong \angle K $ and $ PR $ corresponds to $ JL $. - This statement is **correct** because $ \angle Q $ does correspond to $ \angle K $, and $ PR $ corresponds to $ JL $. Therefore, the only correct statement among the options you provided is: - The fourth statement: $ \angle Q \cong \angle K $ and $ PR $ corresponds to $ JL $.