Download Conditions for Parallelograms

T e ac h i n g T r a n s pa r e n cy
6-3
Conditions for
Parallelograms
Theorems
Conditions for Parallelograms
THEOREM
EXAMPLE
B
If one pair of opposite sides
of a quadrilateral are parallel
and congruent, then the
quadrilateral is a parallelogram.
(quad. with pair of opp. sides and → )
C
D
A
B
If both pairs of opposite sides of a
quadrilateral are congruent, then the
A
quadrilateral is a parallelogram.
(quad. with opp. sides → )
C
D
If both pairs of opposite angles of a
B
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
A
quad.
with
opp.
→
)
(
Theorems
D
Conditions for Parallelograms
THEOREM
EXAMPLE
If an angle of a quadrilateral
is supplementary to both of its
consecutive angles, then the
quadrilateral is a parallelogram.
(quad. with ∠ supp. to cons. → )
If the diagonals of a quadrilateral
bisect each other, then the
quadrilateral is a parallelogram.
(quad. with diags. bisecting
each other → )
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C
126
B
A
x˚
C
(180 - x)˚
(180 - x)˚
D
B
C
Z
A
D
Holt McDougal Geometry