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Prove a quadrilateral is a parallelogram

Criteria needed to prove a shape is a parallogram

There are 5 distinct ways to know that a quadrilateral is a paralleogram. If a quadrilateral meets any of the 5 criteria below, then it must be a parallelogram.

Criteria proving a quadrilateral is parallelogram

  • 1) If a quadrilateral has one pair of sides that are both parallel and congruent.
  • 2) If all opposite sides of the quadrilateral are congruent.
  • 3) Both pairs of opposite sides are parallel.
  • 4) Opposite angles are congruent.
  • 5) Diagonals bisect.
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