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Proving a Quadrilateral is a Parallelogram

1) show both pairs of opposite sides are parallel

2) show both pairs of opposite sides are congruent

3) show both pairs of opposite angles are congruent

4) show one pair of opposite sides are congruent and parallel

5) show the diagonals bisect each other

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Rhombus Corollary

-must have 4 congruent sides

-diagonals must be perpendicular

-diagonals bisect a pair of opposite angles

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Rectangle Corollary

-must have 4 right angles

-diagonals are congruent

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Square Corollary

-must have 4 congruent sides

-must have 4 right angles

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Trapezoid Corollary

-bases must be parallel

-if isosceles, each pair of base angles must be congruent, or a pair of base angles must be congruent, or diagonals must be congruent

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Kite Corollary

-two pairs of consecutive congruent sides, but opposire sides are not congruent

-diagonals are perpendicular

-exactly one pair of opposite angles are congruent

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