Proving Quadrilaterals are Parallelograms

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Example
K
J
6cm
L
8cm
60
20
G
H
Find JH KH m lt KJH
m lt JKH m lt KGJ
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Example Find m lt W
W
Z
3x 18
4x - 9
X
Y
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Proving Quadrilaterals are Parallelograms

• Objective Use theorems to prove quadrilaterals
  are parallelograms

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• By definition, if both pairs of opposite sides
  of a quadrilateral are parallel, then the
  quadrilateral is a parallelogram.

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

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• If both pairs of opposite angles of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.

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• If an angle of a quadrilateral is supplementary
  to both of its consecutive angles, then the
  quadrilateral is a parallelogram.

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A is supplementary to B and D B is
supplementary to A and C

• A
  B

C is supplementary to B and D D is supplementary
to A and C
D
C
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• If the diagonals of a quadrilateral bisect each
  other then the quadrilateral is a parallelogram.

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• If one pair of opposite sides of a
  quadrilateral are congruent and parallel, then
  the quadrilateral is a parallelogram.

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