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 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

Here's how to complete the two-column proof with the appropriate statements and reasons:

**Statements:**
1. a ∥ b and e ∥ f
2. m∠5 + m∠6 = 180° and m∠9 + m∠11 = 180°
3. m∠13 + m∠6 = 180° and m∠13 + m∠11 = 180°
4. m∠6 = m∠11

**Reasons:**
1. given
2. definition of linear pair
3. corresponding angles theorem
4. Transitive Property of Equality

So the completed proof looks like this:

| 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° | corresponding angles theorem |
| 4. m∠6 = m∠11 | Transitive Property of Equality |

This arrangement proves that angles ∠6 and ∠11 are congruent in the parallelogram.