Geometry Section 2-1 1112

CHAPTER 2Reasoning and Proof

Wednesday, October 15, 14

SECTION 2-1Inductive 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. Inductive Reasoning: Coming to a conclusion based off of specific examples and observations

2. Conjecture:

3. Counterexample:


VOCABULARY


2. Conjecture: The conclusion reached from using inductive reasoning

3. Counterexample:


VOCABULARY


2. Conjecture: The conclusion reached from using inductive reasoning

3. Counterexample: A false example that shows the conjecture is not true


EXAMPLE 1Write 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




a. 7, 10, 13, 16 b. 3, 12, 48, 192

Conjecture: The nth term is found by adding 3 to the previous term




a. 7, 10, 13, 16 b. 3, 12, 48, 192


19




a. 7, 10, 13, 16 b. 3, 12, 48, 192


19

Conjecture: The nth term is found by multiplying the

previous term by 4




a. 7, 10, 13, 16 b. 3, 12, 48, 192


19

Conjecture: The nth term is found by multiplying the

previous term by 4

768




c.




c.

Conjecture: The nth figure is found by rotating the previous figure 90° counterclockwise




c.

Conjecture: The nth figure is found by rotating the previous figure 90° counterclockwise


EXAMPLE 2Make 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




a. The product of an odd and even numberTest out some examples to see what happens





3*2 = 6





3*2 = 6 17*4 = 68





3*2 = 6 17*4 = 68 5*10 = 50





3*2 = 6 17*4 = 68 5*10 = 50

Conjecture: The product of an odd and even number will be even




b. The radius and diameter of a circle




b. The radius and diameter of a circleTest out some examples to see what happens

















Conjecture: The diameter is twice as long as the radius


EXAMPLE 3The 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 3The 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 4Based 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%





County

Population

Rate


2,163 371,825 713,126 33,201 50,436 9,402

3.7% 7.2% 7.0% 4.3% 11.3% 6.1%





County

Population

Rate


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


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Geometry Section 2-1 1112

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