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 Skip to navigation

Answer 1

To organize the proof that angles ∠6 and ∠11 are congruent in the given parallelogram where lines a and b are parallel, and lines e and f are parallel, we put the statements in the correct order with their corresponding reasons.

Here's how the proof can be structured:

| 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° | Same-side interior angles are supplementary | | 4. m∠5 + m∠6 = m∠9 + m∠11 | Transitive Property of Equality | | 5. m∠6 = m∠11 | Substitution (if m∠5 + m∠6 = m∠9 + m∠11) | | 6. ∠6 ≅ ∠11 | Definition of congruence (angles) |

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