Alternate Interior Angles Theorem
figure 8
Match the justifications for each step in order to prove the Alternate Interior Angles Theorem. Note that lines l and n are parallel.
(2 points)
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l∥n
∠2≅∠6
∠4≅∠2
∠6≅∠4
1. l and n are parallel (Given)
2. ∠2 and ∠6 are corresponding angles formed by a transversal intersecting l and n (Definition of corresponding angles)
3. ∠2 and ∠6 are congruent (Corresponding angles theorem)
4. ∠4 and ∠2 are alternate interior angles formed by a transversal intersecting l and n (Definition of alternate interior angles)
5. ∠4 and ∠2 are congruent (Alternate interior angles theorem)
6. ∠6 and ∠4 are alternate interior angles formed by a transversal intersecting l and n (Definition of alternate interior angles)
7. ∠6 and ∠4 are congruent (Alternate interior angles theorem)