Parallelogram Proofs Quick Check

Question

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Question
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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)
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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°
Response area
5. Response area Transitive Property of Equality
6. m∠6=m∠11

Answer 1

To complete Sylvia's proof that the opposite angles, ∠6 and ∠11, are congruent in the parallelogram, we can arrange the statements and reasons as follows:

| 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 | | 2. 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 |

So the completed proof would read as follows:

1. Given: a∥b and e∥f
2. Definition of Linear Pair: m∠5 + m∠6 = 180° and m∠9 + m∠11 = 180°
3. Corresponding Angles Theorem: m∠5 = m∠9
4. Definition of Linear Pair: m∠13 + m∠6 = 180° and m∠13 + m∠11 = 180°
5. Transitive Property of Equality: m∠6 = m∠11

This proof logically establishes that ∠6 and ∠11 are congruent.