Chapter 6 Section 6.3

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Chapter 6Section 6.3

• Proving Quadrilaterals Are Parallelograms

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Quick Review
Some Properties of Parallelograms
Definition A parallelogram is a quadrilateral
with both pairs of opposite sides congruent
If a quadrilateral is a parallelogram, then
Theorem 6.2
Theorem 6.3
Theorem 6.4
Theorem 6.5
both pairs of opposite sides are congruent
both pairs of opposite angles are congruent
consecutive angles are supplementary
diagonals bisect each other
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Theorem
Theorem 6.6
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram
Quadrilateral PQRS with both pairs of opposite
sides congruent
PQRS is a parallelogram
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Theorem
Theorem 6.7
If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram
Quadrilateral PQRS with both pairs of opposite
angles congruent
PQRS is a parallelogram
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Theorem
Theorem 6.8
If an angle of a quadrilateral is supplementary
to both of its consecutive angles, then the
quadrilateral is a parallelogram
m?S m?P 180 and m?S m?R 180
PQRS is a parallelogram
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Theorem
Theorem 6.9
If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a parallelogram
PQRS is a parallelogram
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Theorem
Theorem 6.10
If one pair of opposite sides of a quadrilateral
are congruent and parallel, then the
quadrilateral is a parallelogram
PQRS is a parallelogram
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Yes, one pair of opposite sides congruent and
parallel
Yes, diagonals bisect each other
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Yes, both pairs of opposite sides congruent
No, same pair of opposite sides must be parallel
and congruent
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Yes, could show both pairs of opposite sides are
parallel
Yes, Consecutive angles are supplementary
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Definition
Theorem 6.10
Theorem 6.6
Theorem 6.10
Definition
Theorem 6.10
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Theorem 6.9
Theorem 6.8
m?CDA m?DCB 180 OR m?DAB m?ABC 180
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For a Quadrilateral to be a parallelogram
opposite sides must be congruent
3x 6
x 2 y - 1
x 2
2 2 y 1 4 y 1 5 y
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For a Quadrilateral to be a parallelogram
opposite angles must be congruent
2x 70
3x 5 x 3y
x 35
3(35) 5 35 3y 110 35 3y 75 3y 25 y
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For a Quadrilateral to be a parallelogram
diagonals must bisect each other
3x 12
x y 5y
x 4
4 y 5y 4 4y 1 y
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2. Def. ? ?s
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2. Def. ? ?s
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HW 68Pg 342-345 10-26 Even, 30, 32, 34-37
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