Parallelogram
: If a quadrilateral has both pairs of opposite sides parallel then it is a
parallelogram
Properties:
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If a quadrilateral is a parallelogram then it has both pairs of opposite sides parallel
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If a quadrilateral is a parallelogram then it has both pairs of opposite sides congruent
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If a quadrilateral is a parallelogram then it has both pairs of opposite angles congruent
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If a quadrilateral is a parallelogram then it has diagonals that bisect each other
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If a quadrilateral is a parallelogram then it has one pair of opposite sides parallel and
congruent
Ways to Prove:
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If a quadrilateral has both pairs of opposite sides parallel (definition)
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If a quadrilateral has both pairs of opposite sides congruent
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If a quadrilateral has both pairs of opposite angles congruent
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If a quadrilateral has diagonals that bisect each other
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If a quadrilateral has one pair of opposite sides parallel and congruent
Rhombus
: If a parallelogram has two adjacent sides congruent, then it is a rhombus.
Properties:
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If a quadrilateral is a rhombus, then all sides are congruent.
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If a quadrilateral is a rhombus, then the diagonals are perpendicular.
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If a quadrilateral is a rhombus, then the diagonals bisect the angle to which they are
drawn.
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If a quadrilateral is a rhombus, then the diagonals are perp. bisectors of each other
Ways to Prove:
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If a quadrilateral is a parallelogram with 2 adjacent sides congruent, then the
quadrilateral is a rhombus.
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If a quadrilateral has all sides congruent, then the quadrilateral is a rhombus.
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If a quadrilateral is a parallelogram whose diagonals are perpendicular to each other,
then the quadrilateral is a rhombus.
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If a quadrilateral is a parallelogram with a diagonal that bisects the angle to which it is
drawn, then the quadrilateral is a rhombus.
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If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is
a parallelogram
**All properties of a parallelogram
Rectangle:
If a parallelogram has at least one right angle, then it is a rectangle.
Properties:
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If a quadrilateral is a rectangle, then all angles are right angles.
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If a quadrilateral is a rectangle, then the diagonals are congruent.
Ways to prove:
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If a quadrilateral is a parallelogram with one right angle, then the quadrilateral is a
rectangle.
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If a quadrilateral has all angles right angles, then the quadrilateral is a rectangle.
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If a quadrilateral is a parallelogram whose diagonals are congruent, then the
quadrilateral is a rectangle.
**All properties of a parallelogram
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