If two lines are cut by a transversal in such a way that alternate interior angles
are congruent, then the lines are parallel.
given: use the lines and angles numbering system shown on page 156 in your online textbook.
alternate interior angles ∠3 and ∠6 are congruent ( ∠3 ≅ ∠6 ).
prove: the horizontal lines in the figure are parallel.
proof:
statements -
1. ∠3≅∠6
2. m∠3 = m∠6
3. ∠3 and ∠4 are a pair.
4. m∠3 + m∠4 = 180°
5. m∠6 + m∠4 = 180°
6. ∠4 and ∠6 are
7. ∠4 and ∠6 are same-side angles.
8. the horizontal lines in the figure are
reasons -
1. given
2. congruence postulate (think it’s angle)
3. definition of pair.
4. pair property ( think linear)
5. property.
6. definition of angles
7. of same-side angles
8. converse of same-side alternate angles theorem.
! i’m open to learning and any is appreciated !