Consider the case when the transversal is EB and when it is AG.
∠ FCJ and ∠ DFC are alternate interior angles.
∠ FCJ and ∠ CJH are alternate interior angles.
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Two angles are alternate interior angles when they lie between the two lines and on the opposite side of the transversal. Depending on which line is considered the transversal, we will get different answers. Let's first imagine that EB is the transversal. In this case, ∠ DFC is the alternate interior angle. Like ∠ FCJ, it is between the lines but on opposite sides of the transversal.
Let's now imagine that AG is the transversal. In this case, ∠ CJH is the alternate interior angle to ∠ FCJ. Like ∠ FCJ, it is between the lines but on opposite sides of the transversal
