In the diagram, \( a \| b \) and \( e \| f \). Sylvia writes a proof to prove that opposite angles, \( \angle 6 \) and \( \angle 11 \), are congruent in the statements and reasons into their correct locations in the two-column proof. (2 points)

When \( a \parallel b \) and \( e \parallel f \), several properties of parallel lines come into play, particularly when transversal lines intersect them. Opposite (or vertical) angles are always congruent. To show that \( \angle 6 \) and \( \angle 11 \) are congruent, Sylvia can construct the proof as follows: 1. **Statement 1**: \( a \parallel b \) and \( e \parallel f \) (Given) **Reason 1**: This is the given information. 2. **Statement 2**: \( \angle 6 \) and \( \angle 7 \) are corresponding angles. **Reason 2**: When a transversal intersects two parallel lines, corresponding angles are formed. 3. **Statement 3**: \( \angle 6 \cong \angle 7 \) (by Corresponding Angles Postulate) **Reason 3**: Corresponding angles are congruent when the lines are parallel. 4. **Statement 4**: \( \angle 7 \) and \( \angle 11 \) are vertically opposite angles. **Reason 4**: Vertical angles are formed when two lines intersect. 5. **Statement 5**: \( \angle 7 \cong \angle 11 \) (by Vertical Angles Theorem) **Reason 5**: Vertical angles are always congruent. 6. **Statement 6**: \( \angle 6 \cong \angle 11 \) (Transitive property of congruence) **Reason 6**: If \( \angle 6 \) is congruent to \( \angle 7 \) and \( \angle 7 \) is congruent to \( \angle 11 \), then \( \angle 6 \) must be congruent to \( \angle 11 \). Thus, Sylvia has proofed that \( \angle 6 \) and \( \angle 11 \) are congruent through logical reasoning and the properties of parallel lines and angles.