6' Show that consecutive angles are supplementary

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6. Show that consecutive angles are supplementary
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What Makes a Quadrilateral a Parallelogram?
What do you see?
Are both pairs of opposite sides parallel?
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In This Picture
Is one pair of opposite sides congruent and
parallel?
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Are both pairs of opposite sides congruent?
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Are both pairs of opposite angles congruent?
What is this Picture?
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What is this?
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What is this?
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Is a Pentagon a Parallelogram?
NO!
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for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
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for Examples 2 and 3
GUIDED PRACTICE
What theorem can you use to show that the
quadrilateral is a parallelogram?
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for Examples 2 and 3
GUIDED PRACTICE
SOLUTION
Add 3x to each side
Divide each side by 5
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6. Show that consecutive angles are supplementary
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Game Time Name that Theorem
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Game Time Name that Theorem
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Game Time Name that Theorem
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Game Time Name that Theorem
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Game Time Name that Theorem
6. Show that consecutive angles are supplementary
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Game Time Name that Theorem
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EXAMPLE 4
Use coordinate geometry
SOLUTION
One way is to show that a pair of sides are
congruent and parallel. Then apply Theorem 8.9.
AB
CD
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EXAMPLE 4
Use coordinate geometry
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EXAMPLE 4
for Example 4
GUIDED PRACTICE
6. Refer to the Concept Summary. Explain how
other methods can be used to show that
quadrilateral ABCD in Example 4 is a
parallelogram.
SOLUTION
Find the Slopes of all 4 sides and show that each
opposite sides always have the same slope and,
therefore, are parallel.
Find the lengths of all 4 sides and show that the
opposite sides are always the same length and,
therefore, are congruent.
Find the point of intersection of the diagonals
and show the diagonals bisect each other.
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EXAMPLE 4
for Example 4
GUIDED PRACTICE
K
DK and TA are congruent and parallel. So, TDKA is
a parallelogram by Theorem 8.9.
A
D
T
DK
TA
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In Conclusion
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Dont forget your homework.

• Pg 526 1-3, 11-14

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