Download Section 2.1 to 2.2

Warm Up
Describe the pattern and sketch the next
figure.
1.)
Adds one more side to the polygon.
2.)
Face rotates 90 degrees clockwise.
Geometry
Sections 2.1, 2.2
Use Inductive Reasoning and
Analyze Conditional Statements
Describe a Number
Pattern
Describe the pattern in the numbers and find the next
number in the sequence.
1.) 3, 6, 12, 24, 48
Multiply by 2
2.) 0, 1, 4, 9, 16, 25, 36
Perfect squares
Vocabulary
• Conjecture: An unproven statement
that is based on observations.
• You use inductive reasoning when
you find a pattern in specific cases
and then write a conjecture for the
general case.
Conjecture/
Counterexamples
• Use these sums of odd integers:
3+7=10, 1+7=8, 17+21=38
Conjecture: The sum of any two
odd integers is__ even _______.
Vocabulary
• Counterexample: An example that
proves a conjecture is false.
*Example:
•Conjecture: The sum of two
numbers is always greater than
the larger number.
Counterexample: -3 + -2 = -5
Conjecture/
Counterexamples
• Show the conjecture is false by
finding a counterexample.
–If the product of two numbers is
positive, then the two numbers
must both be positive.
-8 * -2 = 16
Vocabulary
Conditional statement:
a logical statement that has two
parts, a hypothesis and a conclusion.
When a conditional statement is written
in if-then form the “if” part contains the
hypothesis and the “then” part contains
the conclusion.
If hypothesis, then conclusion.
Conditional Statements
Rewrite statement in if-then form:
Guitar players are musicians
If you are a guitar player then
you are a musician.
Conditional Statement
Rewrite the statement in if-then form:
An even number is divisible by two.
If a number is even, then it is divisible by
two.
Converse
The converse of a conditional statement
is formed by switching the conclusion
and the hypothesis.
Conditional Statement:
If you are a guitar player then you are a
musician.
Converse:
If you are a musician then you are a guitar
player.
Converse Example
Write the converse of:
If a number is even, then it is divisible by
two.
Converse: If a number is divisible by
two, then it is an even number.
Inverse
The inverse of a conditional statement
is when you negate the hypothesis and
the conclusion. (Turn them into nots)
Conditional Statement:
If you are a guitar player then you are a
musician.
Inverse:
If you are not a guitar player than you are not a
musician.
Inverse Example
Write the Inverse of:
If a number is even, then it is divisible by
two.
Inverse: If a number is not even,
then it is not divisible by two.
Contrapositive
The contrapositive of a conditional
statement is when you negate the
hypothesis and conclusion of the
converse statement.
Converse Statement:
If you are a musician, then you are a guitar
player.
Contrapositive:
If you are not a musician, then you are not a
guitar player
Contrapositive Example
Write the contrapositive of:
If a number is divisible by two, then
it is an even number.
Contrapositive: If a number is not
divisible by two, then it is not an even
number.
Related Conditionals
• Conditional statement:
If hypothesis, then conclusion.
• Inverse:
If not hypothesis, then not
conclusion.
• Converse:
If conclusion, then hypothesis.
• Contrapositive:
If not conclusion, then not
hypothesis.
Write the inverse, converse, &
contrapositive.
• Conditional:
If water is frozen, then its temp is below
zero.
• Inverse:
If water is not frozen, then its temp is not
below zero.
• Converse:
If the temp is below zero, then water is
frozen.
• Contrapositive:
If the temp is not below zero, then the
water
is not frozen.
Homework:
• Page 67- 68
• #6-10(evens),16, 17
• Page 74
• #3-6