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Parallelograms
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Sufficient Conditions for Quadrilaterals to Be Parallelograms

Another sufficient condition for a quadrilateral to be a parallelogram is that two of its sides are parallel and congruent.

Theorem.
If two sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Given:
 Quadrilateral ABCD with AB __ ∥ DC __ and AB __ ≅ CD __
Prove: Quadrilateral ABCD is a parallelogram.


Proof:


In summary, the following are the sufficient conditions for a parallelogram:
  • Two pairs of opposite sides are congruent.
  • Two pairs of opposite angles are congruent.
  • One angle is supplementary to each of the two angles adjacent to it.
  • Diagonals bisect each other.
  • Two sides are parallel and congruent.