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Alternate Interior Angles

The term alternate interior angles is often used when two lines are cut by a third line, a transversal .

Two parallel lines cut by a transversal n, with angles labeled 1 through 8

In the figure above, line t is a transversal cutting lines k and l , and there are two pairs of alternate interior angles:

2 and 8

3 and 5

The Alternate Interior Angles Theorem states that if k and l are parallel , then the pairs of alternate interior angles are congruent . That is,

2 8 and 3 5 .

The converse of this theorem is also true.