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

Answer 1

To prove that the opposite angles, ∠6 and ∠11, are congruent in the parallelogram, you can set up the two-column proof as follows:

| Statements | Reasons |
|---------------------------------------------|-----------------------------------------|
| 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 |

So the responses to drag and drop into the proof are as follows:
- Statement 2: "m∠5 = m∠9"
- Statement 4: "m∠13+m∠6=180° and m∠13+m∠11=180°"
- Statement 5: "m∠6 = m∠11"

Make sure to place each response in the correct row based on the corresponding step in the proof!