f 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.
Please help ! I’m open to learning and any help is appreciated !