Download Geometry 2.3 Law of Syllogism Notes

Geometry 2.3 Law of Syllogism Notes
October 24, 2015
Agenda:
Law of Syllogism Projects Due!!!
- Warm-Up (Writing conditional
statements)
Big Ideas:
- How do we use the Law of
Syllogism to draw a logical
conclusion?
- Writing a two-column proof using algebraic properties to
justify our reasoning
- HW Quiz #2.2 (Per. 3 only)
- Connect the Law of Syllogism
to drawing logical conclusions in
geometry
- Writing a two-column proof
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
10/22 Warm-Up
• For the given statement, write the if­then form and the converse: Sophomores can take driving lessons.
(Hint: If a ________is a _________, then __________________) • Write the 2 conditional statements contained within the following bi­conditional l statement: Points are coplanar
if and only if the points lie on the same plane
.
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
What is a counterexample?
An example that shows a statement is false.
What is a counterexample that would prove that the converse from
our warm-up is false?
You can be a freshman and take drivers ed ­ as long as you are 15
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
Can you think of a counterexample that shows that this is false?
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Geometry 2.3 Law of Syllogism Notes
If
If
Janelle gets
a job
Janelle can
afford a car.
October 24, 2015
,then
Janelle can
afford a car.
,then
Janelle can drive
to school.
Therefore,
Janelle can drive
Janelle gets
,then to school.
If a job
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
If
3x - 4 = 8
,then
3x = 12
If
3x = 12
,then
x = 4.
Therefore,
If 3x - 4 = 8
,then
x = 4.
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
two angles form
the two angles
If a linear pair ,then
are supplementary
the sum of the
the two angles
If are supplementary,then angles is 180
degrees.
Therefore,
the sum of the
two angles form
angles is 180
,then
If a linear pair
degrees.
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
If
a polygon is
regular
,then
the polygon is
equilateral
If
a polygon is
regular
,then
the polygon is
equiangular.
Why can't we make a valid conclusion?
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Geometry 2.3 Law of Syllogism Notes
Law of Syllogism
If P ,then Q
If Q ,then R.
Therefore,
If P ,then R.
October 24, 2015
P
Q
Q
R
P
R
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Geometry 2.3 Law of Syllogism Notes
October 24, 2015
Use the true statements below to
determine whether you know if the
four conclusions below are true or
false. Explain your reasoning.
1.
2.
3.
4.
Group Problem - each
student complete the
problem but work
together in your groups one paper per group will
be graded...
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