Question

Consider parallel lines cut by a transversal. Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answer 1

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

Answer:

Corresponding angle theorem, vertical angle theorem, and the transitive property of congruence.

Step-by-step explanation:

Considering a set of parallel lines cut by a transversal. (Refer the attached image).

Now that lines J and K are parallel, then by "corresponding angle theorem"

$\angle 1=\angle 5$

By "vertical angle theorem"

$\angle 5 = \angle 7$

Using, "transitive property of congruence"

$\angle 1 = \angle 7$

And that is our required proof. In this whole proof we have used "corresponding angle theorem", "vertical angle theorem", and the "transitive property of congruence".