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.

Answer 1

To prove that angles ∠6 and ∠11 are congruent in a parallelogram where lines a and b are parallel and lines e and f are parallel, we can set up a two-column proof. Below is a typical structure for such a proof.

Statements | Reasons --- | ---

1. a ∥ b and e ∥ f | 1. Given
2. Consider the transversal line that intersects lines a and b, along with lines e and f. | 2. Definition of parallel lines (alternate interior angles)
3. By transversal properties, ∠6 and ∠10 are congruent. | 3. Alternate interior angles theorem
4. By transversal properties, ∠10 and ∠11 are congruent. | 4. Alternate interior angles theorem
5. Therefore, ∠6 ≅ ∠11 | 5. Transitive property of congruence

You can adjust the numbering or add more specific details, based on the exact configuration of angles in your diagram. But generally, these statements and reasons together form a coherent proof demonstrating the congruency of ∠6 and ∠11 in the context of a parallelogram formed by the intersecting parallel lines.