6.3 Showing Quadrilaterals are
Parallelograms
Textbook pg 316
What are the
properties of a
parallelogram?
Once we know we are dealing
with a parallelogram, we can
apply all of those properties to the
parallelogram.
How do we determine if the
quadrilateral is a parallelogram in
the first place if no one tells us?
Definition of a Parallelogram: a
quadrilateral with both pairs of opposite
sides parallel
Parallelogram 
If both pairs of opposite sides of a
quadrilateral are congruent, then it
is a parallelogram
Parallelogram 
If both pairs of opposite angles of a
quadrilateral are congruent, then it
is a parallelogram
Parallelogram 
If all pairs of consecutive angles of
a quadrilateral are supplementary,
then it is a parallelogram
xo
yo
xo + yo = 180o
yo
xo
Parallelogram 
If the diagonals of a quadrilateral
bisect EACH OTHER, it is a
parallelogram
Parallelogram 
Practice Problems on pg 317 & 319
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1) Yes, opposite sides are congruent
2) No, opposite angles are not congruent OR
ALL consecutive angles are not necessarily
supplementary
3) No, opposite sides are not congruent
4) No, opposite angles are not congruent
5) Yes, opposite angles are congruent AND
consecutive angles are supplementary
6) Yes, diagonals bisect each other
7) No, diagonals do not bisect each other
Homework
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Assignment # 12
Pg 320 problems 1-21 all, 28-44 all