To complete the two-column proof demonstrating that angles 26 and 11 are congruent in the parallelogram formed by the parallel lines and transversal lines, we can fill in the missing statements and reasons based on geometry principles.
Here is the completed proof:
| Statement | Reason | |---------------------------------------------------|---------------------------------------------| | 1. a || b and e || f | Given | | 2. m∠5 = m∠11 | Corresponding Angles Theorem | | 3. m∠5 + m∠6 = 180º and m∠9 + m∠11 = 180º | Definition of Linear Pair | | 4. m∠6 = m∠9 | Alternate Interior Angles Theorem | | 5. m∠5 + m∠6 = m∠9 + m∠11 | Transitive Property of Equality | | 6. m∠6 = m∠11 | Substitution Property |
In this proof:
- The first statement simply references the given parallel lines.
- The second statement comes from the fact that angle 5 and angle 11 are corresponding angles and therefore equal.
- The third statement states the linear pairs created by the transversal intersecting with the parallels.
- The fourth statement indicates equality between angles 6 and 9 due to alternate interior angles being equal.
- The fifth statement utilizes the transitive property to relate these angle sums.
- The final statement concludes that angles 6 and 11 are equal, completing the proof of their congruence.
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