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.
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.
Transitive Property of Equality
6. m∠6=m∠11

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Answer 1

Here’s how to complete the proof showing that the opposite angles ∠6 and ∠11 are congruent in the parallelogram:

| 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∠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 | | 6. ∠6 ≅ ∠11 | Definition of Congruent Angles |

You can drag and drop the correct statements and reasons into the provided proof structure based on the numbers indicated above.