Geometry Section 2-1 1112

CHAPTER 2
Reasoning and Proof
Wednesday, October 15, 14

SECTION 2-1
Inductive Reasoning and Conjecture

ESSENTIAL QUESTIONS
How do you make conjectures based on inductive
reasoning?
How do you find counterexamples?

VOCABULARY
1. Inductive Reasoning:
2. Conjecture:
3. Counterexample:

VOCABULARY
1. In d u c t i v e R e a s o n i n g : Coming to a conclusion based off of
specific examples and observations
2. Conjecture:
3. Counterexample:

VOCABULARY
2. C o n j e c t u r e : The conclusion reached from using inductive
reasoning
3. Counterexample:

VOCABULARY
2. C o n j e c t u r e : The conclusion reached from using inductive
reasoning
3. C o u n t e r e x a m p l e : A false example that shows the conjecture is
not true

EXAMPLE 1
Write the conjecture that describes the pattern in each
sequence. Then use your conjecture to find the next item
in the sequence.
a. 7, 10, 13, 16 b. 3, 12, 48, 192

EXAMPLE 1
in the sequence.
a. 7, 10, 13, 16 b. 3, 12, 48, 192
Conjecture: The nth
term is found by
adding 3 to the
previous term

EXAMPLE 1
in the sequence.
a. 7, 10, 13, 16 b. 3, 12, 48, 192
Conjecture: The nth
term is found by
adding 3 to the
previous term
19

EXAMPLE 1
in the sequence.
a. 7, 10, 13, 16 b. 3, 12, 48, 192
Conjecture: The nth
term is found by
adding 3 to the
previous term
19
Conjecture: The nth
term is found by
multiplying the
previous term by 4

EXAMPLE 1
in the sequence.
a. 7, 10, 13, 16 b. 3, 12, 48, 192
Conjecture: The nth
term is found by
adding 3 to the
previous term
19
Conjecture: The nth
term is found by
multiplying the
previous term by 4
768

EXAMPLE 1
in the sequence.
c.

EXAMPLE 1
in the sequence.
c.
Conjecture: The nth figure is found by rotating the previous
figure 90° counterclockwise

EXAMPLE 2
Make a conjecture about each value or geometric
relationship. List or draw some examples that support
your conjecture.
a. The product of an odd and even number

EXAMPLE 2
your conjecture.
Test out some examples to see what happens

EXAMPLE 2
your conjecture.
3*2 = 6

EXAMPLE 2
your conjecture.
3*2 = 6 17*4 = 68

EXAMPLE 2
your conjecture.
3*2 = 6 17*4 = 68 5*10 = 50

EXAMPLE 2
your conjecture.
3*2 = 6 17*4 = 68 5*10 = 50
Conjecture: The product of an odd and even number will
be even

EXAMPLE 2
your conjecture.
b. The radius and diameter of a circle

EXAMPLE 2
your conjecture.

EXAMPLE 2
your conjecture.
Conjecture: The diameter is twice as long as the radius

EXAMPLE 3
The table shows the total sales for the first three months
that Matt Mitarnowski’s Wonderporium is open. Matt
wants to predict the sales for the fourth month.
Month
Sales
1 2 3
$400 $800 $1600
Make a conjecture about the sales in the fourth month
and justify your claim.

EXAMPLE 3
The table shows the total sales for the first three months
that Matt Mitarnowski’s Wonderporium is open. Matt
wants to predict the sales for the fourth month.
Month
Sales
1 2 3
$400 $800 $1600
Make a conjecture about the sales in the fourth month
and justify your claim.
Conjecture: The sales double each month, so the fourth
month should have $3200 in sales

EXAMPLE 4
Based on the table showing unemployment rates for
various counties in Texas, find a counterexample for the
following statement: The unemployment rate is highest in the
cities with the most people.
County
Population
Rate
Armstrong Cameron El Paso Hopkins Maverick Mitchell
2,163 371,825 713,126 33,201 50,436 9,402
3.7% 7.2% 7.0% 4.3% 11.3% 6.1%

PROBLEM SET

PROBLEM SET
p. 92 #1-45 odd, 50
“Success is the sum of small efforts, repeated day in and
day out.” - Robert Collier

Geometry Section 2-1 1112

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Geometry Section 2-1 1112