Given: Lines a and b are parallel and line c is a transversal.

Question

Prove: Angle2 is supplementary to Angle8

Horizontal and parallel lines a and b are cut by transversal c. On line a where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line b where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7.
What is the missing reason in the proof?

Statement Reason
1. a || b, c is a transversal 1. given
2. ∠6 ≅ ∠2 2. ?
3. m∠6 = m∠2 3. def. of congruent
4. ∠6 is supp. to ∠8 4. def. of linear pair
5. ∠2 is supp. to ∠8 5. congruent supplements theorem
corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Answer 1

To fill in the missing reason for step 2 of the proof, we need to identify what justifies the statement that \(\angle 6\) is congruent to \(\angle 2\). Since lines \(a\) and \(b\) are parallel and \(c\) is a transversal, \(\angle 6\) and \(\angle 2\) are corresponding angles.

Thus, the appropriate reason for step 2 is:

2. Corresponding Angles Postulate

The updated proof would look like this:

| Statement | Reason | |------------------|----------------------------------| | 1. a || b, c is a transversal | 1. given | | 2. ∠6 ≅ ∠2 | 2. Corresponding Angles Postulate | | 3. m∠6 = m∠2 | 3. def. of congruent | | 4. ∠6 is supp. to ∠8 | 4. def. of linear pair | | 5. ∠2 is supp. to ∠8 | 5. congruent supplements theorem |

In conclusion, the missing reason is the Corresponding Angles Postulate.