Use the image to answer the question.

Question

Two parallel horizontal lines a and b, intersecting with two parallel slanted lines e and f. A parallelogram is formed in the center of the intersecting lines.

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 complete the two-column proof showing that the opposite angles ∠6 and ∠11 are congruent in the parallelogram, you would arrange 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 = 180° - m∠13 and m∠11 = 180° - m∠13 | Corresponding Angles Theorem | | 5. m∠6 = m∠11 | Transitive Property of Equality |

So, for the response areas:

• For step 2, the response should be "definition of linear pair."
• For step 4, the response should be "Corresponding Angles Theorem."
• For step 6, the response is "Transitive Property of Equality."

Thus, the proof would logically show that ∠6 and ∠11 are congruent through the relationships established in these steps.