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!