Lesson Properties of a Parallelogram

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A parallelogram is a specific type of quadrilateral in which both pairs of opposite sides are parallel and congruent. This is not necessarily true for all quadrilaterals, but is true for squares, rectangles, and rhombi.
Options for proving a quadrilateral a parallelogram: (in a proof, only one is necessary; prove whichever is simplest depending on the given information)
- Prove 1 pair of opposite sides parallel and congruent.
- Prove 2 pairs of opposite sides parallel.
- Prove 2 pairs of opposite sides congruent.
- Prove opposite angles congruent.
- Prove consecutive angles supplementary. (adding up to 180 degrees; see definition of supplementary angles)

Similarly, these properties apply and may be used to identify parallelograms from unknown quadrilaterals. Note, however, that the given information must specify that the shape is a quadrilateral (a 4-sided polygon.)
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