Question

In the diagram, a∥b and e∥f . Sylvia writes a proof to prove that opposite angles, ∠6 and ∠11 , are congruent in the parallelogram. Drag and drop the statements and reasons into their correct locations in the two-column proof. (2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statement Reason 1. a∥b and e∥f given 2. Response area Corresponding Angles Theorem 3. m∠5+m∠6=180° and m∠9+m∠11=180° definition of linear pair 4. m∠13+m∠6=180° and m∠13+m∠11=180° Response area 5. Response area Transitive Property of Equality 6. m∠6=m∠11 Response area

Answer 1

To set up the two-column proof regarding the congruence of opposite angles ∠6 and ∠11 in the parallelogram, we can organize the statements and reasons 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∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | definition of linear pair | | 4. m∠6 = m∠11 | Transitive Property of Equality | | 5. m∠5 + m∠6 = m∠9 + m∠11 | Corresponding Angles Theorem | | 6. m∠6 = m∠11 | Conclusion (Angles are congruent) |

You would drag and drop the responses so that they fit correctly into the proof. Remember that in an actual proof context, you are proving that ∠6 and ∠11 are congruent, so you may adjust the placement based on the logical flow, but this layout provides a good foundational organization.