To complete the proof that angles ∠6 and ∠11 are congruent in the parallelogram with the given statements and reasons, the correct order should be as follows:
| Statement | Reason | |------------------------------------------------------|--------------------------------------------| | 1. a∥b and e∥f | given | | 2. m∠5 + m∠6 = 180° and m∠9 + m∠11 = 180° | definition of linear pair | | 3. m∠5 = m∠9 | Corresponding Angles Theorem | | 4. m∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | definition of linear pair | | 5. m∠6 = m∠11 | Transitive Property of Equality | | 6. ∠6 ≅ ∠11 | Definition of Congruence |
Correctly Placed Responses:
- Response 1: 1. a∥b and e∥f | given
- Response 2: 2. m∠5 + m∠6 = 180° and m∠9 + m∠11 = 180° | definition of linear pair
- Response 3: 3. m∠5 = m∠9 | Corresponding Angles Theorem
- Response 4: 4. m∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | definition of linear pair
- Response 5: 5. m∠6 = m∠11 | Transitive Property of Equality
- Response 6: 6. ∠6 ≅ ∠11 | Definition of Congruence
Place the responses in the corresponding response areas to complete the proof successfully.