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

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Answer 1

To complete the two-column proof to show that ∠6 and ∠11 are congruent, you can match the provided statements and reasons accordingly. Here’s how it should look:

| Statement | Reason | |------------------------------------------------|-------------------------------------| | 1. a∥b and e∥f | Given | | 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° | Alternate interior angles theorem | | 5. m∠6=m∠11 | Transitive Property of Equality | | 6. m∠6=m∠11 | Definition of Congruence |

Explanation:

• 1 states the given information about the lines.
• 2 corresponds to the conclusion you reach by saying that angles are linear pairs due to the intersection of the lines.
• 4 mentions alternate interior angles formed by the parallel lines and transversal, which are equal.
• 5 uses the Transitive Property of Equality to create a relationship between ∠6 and ∠11.
• Finally, 6 restates that m∠6 is congruent to m∠11, affirming the goal of the proof.

Adjust or confirm the placement of "Alternate Interior Angles Theorem" as required based on your course material or the context of the original image.