6'3 Proving Quadrilaterals are ograms

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6.3 Proving Quadrilaterals are ograms

• Pg 338

2
Thm 6.6

• If both pairs of opposite sides of a
  quadrilateral are _at_, then the quadrilateral is a
  parallelogram.

A
B
__ __
ABCD is a parallelogram
__
__
C
D
__ __
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Thm 6.7

• If both pair of opposite ?s of a quadrilateral
  are _at_, then the quadrilateral is a ogram.

B
A
((
)
ABCD is a parallelogram
))
(
C
D
4
Thm 6.8

• If an ? of a quadrilateral is supplementary to
  both of its consecutive ?s, then the
  quadrilateral is a ogram.

B
A
(180-x)
x
ABCD is a parallelogram
x
C
D
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Thm 6.9

• If the diagonals of a quadrilateral bisects each
  other, then the quadrilateral is a ogram.

B
A
__
__ __
__
__ __
C
D
ABCD is a parallelogram
6
Thm 6.10

• If one pair of opposite sides of a quadrilateral
  are ? and then the quadrilateral is a ogram.

B
gt
A
ABCD is a parallelogram
gt
C
D
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Exampledetermine whether the a quadrilateral is
a ogram and explain why or why not.
__

• Yes its a ogram because both pair of opposite
  sides are _at_.

__ __
__ __
__
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Example cont.

• Yes because the 2 triangles are ? by SAS post, so
  its a parallelogram because both pairs of sides
  are ?.

B
A
__
)
__
__
(
D
C
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Example cont.

• Yes because its parallelogram by the def of a
  parallelogram.

gt



gt
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Example cont.

• No, because consecutive ?s are not
  supplementary.

65o
65o
110o
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ExampleProve that the pts. represent the
vertices of a ogram

• J (-6,2)
• K(-1,3)
• L(2,-3)
• M(-3,-4)
• Graph then use one of todays theorems and
  distance formula and/or slope formula or use def
  of a parallelogram and slope formula.

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Example cont.Using thm 6.6 and distance formula
JK
ML
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Exampleusing distance formula cont.
JM
Both pairs of opp sides are _at_
KL
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Example contusing the def of ogram and slope
m of JK
m of ML
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Example cont.
m of JM
Opposite side are ll
m of KL
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Assignment