Non congruent alternate interior angles occur when two non parallel lines are intersected by a transversal. In the diagram above, the two legs of the chair act as the non parallel lines while the seat acts as the transversal. If the two legs were parallel, then the alternate interior angles would be congruent. In the real world, congruent alternate interior angles are much more common. Things in the real world, such as a buildings, are normally created with parallel and perpendicular lines because they are more sturdy.
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