Consider parallel lines cut by a transversal. Explain which theorems, definitions, or combinations of both can be used to prove

Since vertical angles are congruent, angles 1 and 4 are congruent. As for corresponding angles congruent, angles 4 and 8 are also congruent. Because angle 4 is congruent to both angles 1 and 8, angle 1 is congruent to angle 8.

Answer:

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

Step-by-step explanation:

In the context of parallel lines intersected by a transversal. (Refer to the attached image).

Given that lines J and K are parallel, according to "corresponding angle theorem"

By "vertical angle theorem"

Utilizing "transitive property of congruence"

Thus, this forms our needed proof. Throughout this proof, we incorporated the "corresponding angle theorem,” “vertical angle theorem,” and the "transitive property of congruence."