Ways to Prove that Quadrilaterals are Parallelograms

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Ways to Prove that Quadrilaterals are
Parallelograms
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Remember!

• Definition of a parallelogram
• A quadrilateral with both
• pairs of opposite sides
• parallel.

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3 Properties

• Opposite sides are congruent.
• Opposite angles are congruent.
• Diagonals bisect each other, but are not
  necessarily congruent.

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• If you have a quadrilateral and want to prove
  that it is a parallelogram you need to show that
• Both pairs of opposite sides are parallel.

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4 Theorems

• 1. If both pairs of opposite sides of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram

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• 2. If one pair of opposite sides of a
  quadrilateral are both congruent and parallel,
  then the quadrilateral is a parallelogram.

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• 3. If both pairs of opposite angles of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.

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• 4. If the diagonals of a quadrilateral bisect
  each other, then the quadrilateral is a
  parallelogram.