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

Question

∠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 . ∠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 . ∠Q≅∠K and PR¯¯¯¯¯¯¯¯ corresponds to JL¯¯¯¯¯¯¯ .

GPT-4o mini · Answer

Since triangles $ \triangle PQR $ and $ \triangle JKL $ are similar (denoted by the symbol $ \sim $), the following properties hold true: 1. Corresponding angles are congruent. 2. Corresponding sides are in proportion. Given this information, we can verify the statements one by one for correctness. 1. **∠P≅∠J and $ PQ $ corresponds to $ JL $**: This is correct because if $ \triangle PQR \sim \triangle JKL $, then $ \angle P $ corresponds to $ \angle J $, and side $ PQ $ corresponds to side $ JL $. 2. **∠P≅∠J and $ QR $ corresponds to $ JK $**: This is also correct, as $ \angle P $ corresponds to $ \angle J $, and side $ QR $ corresponds to side $ JK $. 3. **∠Q≅∠L and $ PQ $ corresponds to $ JK $**: This is not correct, because $ \angle Q $ corresponds to $ \angle K $ (not $ \angle L $), and $ PQ $ corresponds to $ JL $, not $ JK $. 4. **∠Q≅∠K and $ PR $ corresponds to $ JL $**: This statement is correct; $ \angle Q $ corresponds to $ \angle K $, but $ PR $ does not correspond to $ JL $ but rather to $ KL $. Thus, only the first two statements are correct: - ∠P≅∠J and $ PQ $ corresponds to $ JL $. - ∠P≅∠J and $ QR $ corresponds to $ JK $. So, in conclusion, you have two accurate statements regarding the similar triangles $ \triangle PQR $ and $ \triangle JKL $ based on their corresponding angles and sides.