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

Question

1. Statement: a || b and e || f Reason: given
2. Statement: [BLANK] Reason: Corresponding Angles Theorem
3. Statement: m angle 5 + m angle 6 = 180 degrees and m angle 9 + m angle 11 = 180 Reason: definition of linear pair
4. Statement: m angle 13 + m angle 6 = 180 degrees and m angle 13 + m angle 11 = 180 degrees Reason: [BLANK]
5. Statement: [BLANK] Reason: Transitive Property of Equality
6. Statement: m angle 6 = m angle 11 Reason: [BLANK]

Options to fill in blanks:
CPCTC Theorem
Subtraction Property of Equality
m angle 5 + m angle 7 = 180 degrees and m angle 13 + m angle 14 = 180 degrees
m angle 5 = m angle 13 and m angle 9 = m angle 13
Substitution Property of Equality
m angle 13 + m angle 6 = m angle 13 + m angle 11

Answer 1

Here is the completed two-column proof with the statements and reasons filled in appropriately:

1. Statement: \( a \parallel b \) and \( e \parallel f \)
   Reason: Given

2. Statement: \( m \angle 5 + m \angle 7 = 180^\circ \) and \( m \angle 13 + m \angle 14 = 180^\circ \)
   Reason: Corresponding Angles Theorem

3. Statement: \( m \angle 5 + m \angle 6 = 180^\circ \) and \( m \angle 9 + m \angle 11 = 180^\circ \)
   Reason: Definition of Linear Pair

4. Statement: \( m \angle 13 + m \angle 6 = 180^\circ \) and \( m \angle 13 + m \angle 11 = 180^\circ \)
   Reason: Substitution Property of Equality

5. Statement: \( m \angle 13 + m \angle 6 = m \angle 13 + m \angle 11 \)
   Reason: Transitive Property of Equality

6. Statement: \( m \angle 6 = m \angle 11 \)
   Reason: CPCTC Theorem

The proof shows that angles 6 and 11 are congruent by establishing relationships between the angles formed by parallel lines and a transversal, leading to the conclusion through properties of equality.