Question

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answer 1

Sample Response: Because vertical angles are congruent, angles 1 and 4 are congruent. Because corresponding angles are congruent, angles 4 and 8 are congruent. Because angle 4 is congruent to both 1 and 8, angle 1 is congruent to angle 8.

Answer 2

1. The first theorem used is that vertical angles are congruent.
2. The next theorem used is that adjacent angles in a parallelogram are supplementary. 
3. The definition of supplementary angles is then used for angle formed by intersecting  lines.
4. The theorem on vertical angles is used again.
5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.