1. Opener:
Study the following pattern. Row 1: 1
Row 2: 1 1
1. If the pattern is extended, find Row 3: 1 2 1
the terms in row 7. Row 4: 1 3 3 1
Row 5: 1 4 6 4 1
Row 6: 1 5 10 10 5 1
2. Make a conjecture for the pattern.
3. Make a conjecture for the sum of the
terms in each row.
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2. Homework Questions:
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3. 2‐2: Conditional Statements
What are they?
Hypothesis Conclusion
Conditional Statements
Notation Venn Diagram
Examples:
1) If you are 16, then you are a teenager.
2) You live in Illinois, if you live in Northbrook.
Venn Diagrams to represent conditionals:
1) If you are 16, then you are a teenager.
2) You live in Illinois, if you live in Northbrook.
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4. Writing Conditional Statements:
1) Tarantulas are spiders.
2) A 25 degree angle is acute.
Analyzing truth values:
1) If this is September, then the next month is October.
2) If 2 angles are obtuse, then they are congruent.
3) If an even number greater than 2 is prime, then 5 + 4 = 8.
Important conclusion:
If p is true, then ___________________________________
If p is false, then __________________________________
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5. Negation Converse
Related
Conditionals
Inverse Contrapositive
Examples:
1) FACT: Glenbrook North students are Spartans.
Conditional:
Converse:
Inverse:
Contrapositive:
2) Conditional:If m A = 95 degrees, then A is obtuse.
TRUE or FALSE
Converse: TRUE or FALSE
Inverse: TRUE or FALSE
Contrapositive: TRUE or FALSE
Look for the pattern (what kind of reasoning?):
Which statements always have the same truth value?
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6. 2‐3: Deductive Reasoning
A process of using logic to draw conclusions from given facts, definitions, and
properties
How is this different from inductive reasoning?
Inductive or Deductive?
1)
2) There is a myth that birds will abandon their young if you touch them.
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7. Types of Deductive Reasoning
Law of Detachment Law of Syllogism
If p q is a true If p q and q r, are
statement,and p is true, true statements, then
then q is also true. p r is a true statement.
Example: If I oversleep,
Example: If I get over
then I will miss the bus.
a 90%, then I get an A.
If I miss the bus, then I
I got a 96%.
will have to walk to school.
Conjecture: I got an A.
Conjecture: If I oversleep
then I will have to walk to
school.
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8. With your partner, decide whether each of the following examples is valid using
Deductive Reasoning. Then decide which law it is demonstrating. Hold up the
appropriate response cards.
A) Given: If side lengths of a triangle are 5, 12, and 13, then the area of the
triangle is 30.
The area of PQR is 30.
Conjecture: The side lengths of the triangle are 5, 12, and 13.
B) Given: In the World Series, if a team wins 4 games, the team wins the
Series.
In 2004, the Red Sox won 4 games in the World Series.
Conjecture: The Red Sox won the World Series.
C) Given: If a figure is a kite, then it is a quadrilateral. If a figure is a
quadrilateral, then it is a polygon.
Conjecture: If a figure is a kite, then it is a polygon.
D) Given:If a number is divisible by 2, then it is even. If a number is even,
then it is an integer.
Conjecture: If a number is an integer, then it is divisible by 2.
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9. Draw a conclusion using Deductive Reasoning:
A) Given: If 2y = 4, then z = ‐1. If x + 3 = 12, then 2y = 4.
x + 3 = 12.
Conclusion:
B) Given: If the sum of two angles is 180 degrees, then the angles are
supplementary. If 2 angles are supplementary, then they are not the
angles in a triangle.
m<A = 135 degrees and m<B = 45 degrees
Conclusion:
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10. Closer:
For the following scenarios, discuss the given statements, and decide with your
partner if they are an example of a negation, a converse, an inverse, or a
contrapositive.
Then decide whether the statement is true or false. When I call time, one partner
should hold up the statement response card, and the other should hold up the
true/false response card.
Remember, if you think it is false, make sure you have a counterexample!
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11. Conditional: If an animal is a brown bear,
then the animal sleeps for 3 months each year.
Related Statement:
If an animal does not sleep for 3 months each year,
then the animal is not a brown bear.
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12. Conditional: If m A = 95o, then A is obtuse.
Related Statement: If A is obtuse, then m A = 95o.
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13. Yard
Enclosed by a fence
Has a swimming pool
Conditional: If a yard has a swimming pool, then it is enclosed by a fence.
Related Statement: If a yard does not have a swimming pool, then it is not
enclosed by a fence.
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