In both theorems, a pair of angles is formed when two parallel lines are cut by a transversal. However, in the Alternate Interior Angles Theorem, each pair of alternate interior angles that is formed are congruent, whereas in the Consecutive Interior Angles Theorem each pair of angles formed is supplementary.
Practice makes perfect
Let's begin by reviewing the theorems.
Alternate Interior Angles Theorem
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.
Notice that in both theorems a pair of angles is formed when two parallel lines are cut by a transversal. Thus, both can be represented by the following diagram.
However, each theorem gives us a different conclusion.
Consecutive Interior Angles Theorem: ∠ 1 and ∠ 2 are supplementary. ∠ 3 and ∠ 4 are supplementary.
In the Alternate Interior Angles Theorem, each pair of alternate interior angles that is formed is congruent, whereas in the Consecutive Interior Angles Theorem, each pair of angles formed is supplementary.
