In the diagram, a∥b

Question

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

Answer 1

Here's how you can properly fill in the two-column proof for showing that angles ∠6 and ∠11 are congruent in a parallelogram given that lines a and b are parallel and lines e and f are parallel.

| 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∠5 + m∠6 = m∠9 + m∠11 | Transitive Property of Equality | | 5. m∠6 = m∠11 | Substitution Property of Equality |

In this proof:

• You start by establishing the parallel lines.
• Then, you use the definition of a linear pair to show the relationships involving the angles.
• The transitive property allows for equating the angle measures.
• Finally, you conclude that since the measures of angles 6 and 11 are equal, the angles are congruent.

Make sure the text you insert matches the intent of the argument being made in the proof!