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° 5. Response area Transitive Property of Equality 6. m∠6=m∠11 Response area

Answer 1

Here’s how you can organize the proof for congruence of opposite angles ∠6 and ∠11 in the parallelogram:

| 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∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | Response area (fill in here) | | 4. m∠6 = m∠11 | Response area (fill in here) | | 5. m∠6 = m∠11 | Transitive Property of Equality |

You need to fill in the response areas with the appropriate statements from your options. Here's how you should fill out those two areas:

• For the Response area (fill in here) after statement 3, use "Corresponding Angles Theorem."
• For the Response area (fill in here) after statement 4, you will place "m∠13 = m∠13" or the equivalent, indicating the angles are equal as they are corresponding angles.

So to recap, the completed proof with the responses filled in would look like this:

| 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∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | Corresponding Angles Theorem | | 4. m∠6 = m∠11 | Transitive Property of Equality |

This completes the proof, showing that the opposite angles in the parallelogram are congruent.