Left Panel Interactive

Statements

Reasons

1. b || c

1. given

2. a is a transversal
of b and c.

2. given

3. ∠1 & ∠3 form a lin. pr. ∠2 & ∠4 form a lin. pr.

3. def. of linear pair

4. ∠1 & ∠3 are supp. ∠s. ∠2 & ∠4 are supp. ∠s.

4. linear pair postulate

5. m∠1 + m∠3 = 180,
m∠2 + m∠4 = 180

5. def. of supplementary angles

6. ∠1 ≅ ∠5, ∠2 ≅ ∠6

6. corr. angles theorem

7. m∠1 = m∠5,
m∠2 = m∠6

7. def. of congruent angles

8. m∠5 + m∠3 = 180, m∠6 + m∠4 = 180

8. substitution property

9. ∠5 and ∠3 are supp., ∠6 and ∠4 are supp.

9. def. of supplementary angles