Quadrilateral Proofs

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Quadrilateral Proofs
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Quadrilateral Classification
Quadrilateral
Parallelogram
Trapezoid
Rectangle
Rhombus
Isosceles Trapezoid
Square
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Proving a quadrilateral is a parallelogram you
may do any of the following
Prove two pairs of opposite sides parallel
Prove two pairs of opposite sides congruent
Prove one pair of opposite sides both parallel
and congruent
Prove the diagonals bisect each other
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Proving a quadrilateral is a rectangle, first
prove the figure is a parallelogram and then use
one of the following approaches
Prove two adjacent sides perpendicular
Prove one angle is a right angle
Prove the diagonals are congruent
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Proving a quadrilateral is a rhombus, first prove
the figure is a parallelogram and then use one of
the following approaches
Prove one pair of consecutive sides congruent
Prove diagonals bisect the angles
Prove diagonals are perpendicular to each other
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Proving a quadrilateral is a square, first prove
the figure is a parallelogram and then use one of
the following approaches
Prove one pair of consecutive sides congruent
and at least 1 right angle
Prove diagonals bisect the angles and one pair
of consecutive sides is congruent
Prove diagonals are congruent and perpendicular
to each other
Prove diagonals are congruent and one pair of
consecutive sides congruent
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Proving a quadrilateral is a trapezoid
Prove only one pair of opposite sides is
parallel
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Proving a quadrilateral is an isosceles
trapezoid, first prove the figure is a trapezoid
and then use one of the following approaches
Prove the non-parallel sides are congruent
Prove the diagonals are congruent
Prove one pair of base angles are congruent
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Two non-parallel sides are congruent
YES
YES
NO
YES
YES
Two non-congruent sides are parallel
Only Two sides are parallel
YES
YES
YES
YES
YES
YES
NO
YES
YES
NO
YES
YES
YES
NO
YES
NO
YES
YES
NO
YES
YES
NO
YES
NO
NO
NO
YES
NO
10
YES
NO
NO
YES
NO
NO
YES
NO
YES
NO
NO
NO
YES
NO
YES
YES
NO
NO
YES
NO
NO
NO
YES
NO
YES
NO
NO
NO
YES
NO
All angles congruent
All angles congruent
NO
NO
YES
NO