Answer:
The angle pairs that could be used to show that the two lines are parallel are corresponding angles, alternate exterior angles, and alternate interior angles.
Step-by-step explanation:
To show that two lines are parallel when cut by a transversal, we can use congruent angle pairs. The angle pairs that could be used to show parallel lines are:
1. Corresponding angles: Corresponding angles are formed on the same side of the transversal, and on the same side of the two lines being cut. If the corresponding angles are congruent, it can be used to prove that the lines are parallel.
2. Alternate exterior angles: Alternate exterior angles are formed on opposite sides of the transversal, and outside the two lines being cut. If the alternate exterior angles are congruent, it can be used to prove that the lines are parallel.
3. Alternate interior angles: Alternate interior angles are formed on opposite sides of the transversal, and between the two lines being cut. If the alternate interior angles are congruent, it can be used to prove that the lines are parallel.
Note: Consecutive interior angles and consecutive exterior angles are not congruent when the lines are parallel, so they cannot be used to prove parallel lines.
Therefore, the angle pairs that could be used to show that the two lines are parallel are corresponding angles, alternate exterior angles, and alternate interior angles.
