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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

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

Rhombus Corollary

-must have 4 congruent sides

-diagonals must be perpendicular

-diagonals bisect a pair of opposite angles

-diagonals must be perpendicular

-diagonals bisect a pair of opposite angles

Rectangle Corollary

-must have 4 right angles

-diagonals are congruent

-diagonals are congruent

Square Corollary

-must have 4 congruent sides

-must have 4 right angles

-must have 4 right angles

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

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

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

-diagonals are perpendicular

-exactly one pair of opposite angles are congruent