Let's go through the different kinds of pairs of angles there are and how they are related when the lines being crossed are parallel.
Pair of angles
Congruent?
Corresponding angles
Yes
Alternate interior angles
Yes
Alternate exterior angles
Yes
Consecutive Interior angles
No
Corresponding angles have corresponding positions. For example, each angle could be above the line and to the right of the transversal. By the Corresponding Angles Theorem, we know the following angles are congruent.
&∠ 1 ≅ ∠ 5
&∠ 2 ≅ ∠ 6
&∠ 3 ≅ ∠ 7
&∠ 4 ≅ ∠ 8
Alternate interior angles are pairs of angles that lie between the two lines and on opposite sides of the transversal. By the Alternate Interior Angles Theorem, we know the following angles are congruent.
&∠ 3 ≅ ∠ 6
&∠ 4 ≅ ∠ 5
Alternate exterior angles are pairs of angles that lie outside the two lines and on opposite sides of the transversal. By the Alternate Exterior Angles Theorem, we know the following angles are congruent.
&∠ 1 ≅ ∠ 8
&∠ 2 ≅ ∠ 7
