Question

- Write a two-column proof of the Alternate Exterior Angles Theorem(Theorem 3-3).Given: r || sProve: angle 1 = angle 8​

Answer 1

To prove the Alternate Exterior Angles Theorem, we can use the fact that line r is parallel to line s. The theorem states that if a transversal intersects two parallel lines, then the exterior angles on opposite sides of the transversal are congruent. Therefore, angle 1 is congruent to angle 8.

Step-by-step explanation:

To prove the Alternate Exterior Angles Theorem, we need to show that angle 1 is congruent to angle 8.

1. Given that line r is parallel to line s.
2. Alternate Exterior Angles Theorem states that if a transversal intersects two parallel lines, then the exterior angles on opposite sides of the transversal are congruent.
3. Angle 1 and angle 8 are alternate exterior angles formed by transversal with lines r and s.
4. Therefore, angle 1 = angle 8 by the Alternate Exterior Angles Theorem.