Question

Use the image to answer the 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 Reason1. a∥b and e∥f given2. Response area Corresponding Angles Theorem3. m∠5+m∠6=180° and m∠9+m∠11=180° definition of linear pair4. m∠13+m∠6=180° and m∠13+m∠11=180° Response area5. Response area Transitive Property of Equality6. m∠6=m∠11 Response area   Substitution Property of Equalitym∠5=m∠13 and m∠9=m∠13CPCTC Theoremm∠5+m∠7=180° and m∠13+m∠14=180°Subtraction Property of Equalitym∠13+m∠6=m∠13+m∠11

Answer 1

Here is how you can set up the two-column proof for showing that \(\angle 6\) and \(\angle 11\) are congruent in the parallelogram:

| Statement | Reason | |-------------------------------------------------------|----------------------------------------| | 1. \(a \parallel b\) and \(e \parallel f\) | Given | | 2. \(m\angle 5 + m\angle 6 = 180^\circ\) and \(m\angle 9 + m\angle 11 = 180^\circ\) | Definition of linear pair | | 3. \(m\angle 5 = m\angle 13\) and \(m\angle 9 = m\angle 13\) | Corresponding Angles Theorem | | 4. \(m\angle 13 + m\angle 6 = 180^\circ\) and \(m\angle 13 + m\angle 11 = 180^\circ\) | Subtraction Property of Equality | | 5. \(m\angle 13 + m\angle 6 = m\angle 13 + m\angle 11\) | Transitive Property of Equality | | 6. \(m\angle 6 = m\angle 11\) | Substitution Property of Equality |

This organizes the steps, statements, and reasons coherently in a way that logically leads to the conclusion that \(\angle 6\) and \(\angle 11\) are congruent.