# can one assume alterate interior angles?

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If two distinct lines are cut by a third line (called the transversal) in two different points then there are names for the angles formed by the lines and the transversal.

Alternate interior angles are angles that are between the two lines and on alternate (opposite) sides of the transversal.

If the lines that are cut by the transversal are parallel, then alternate interior angles are congruent.

You cannot assume that alternate interior angles are congruent. You know that they are congruent if the lines are parallel, but they are not congruent if the lines are not parallel. Thus you must show (or be given) that the lines are parallel.