Indicate whether the quadrilateral is a parallelogram. Give the theorem name or definition that supports your answer.

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justaguide eNotes educator| Certified Educator

The figure shows a quadrilateral with equal opposite sides and the interior angle made by the two with a third side are 120 degrees and 60 degrees.

As 120 + 60 = 180, the two lines are parallel to each other. This follows from the fact that in the case of two parallel lines intersected by a transversal, the sum of the consecutive interior angles is equal to 180 degrees.

As the opposite sides are parallel as well as equal in length the quadrilateral is a parallelogram.