Download Inductive Reasoning - Hartland High School

Section 2.1 Use Inductive Reasoning
REASONING and PROOF
In this unit, we will learn how to use logical reasoning to draw conclusions and solve problems.
There are many formal techniques and procedures involved in logical reasoning and in proving arguments.
Inductive Reasoning
Geometry, like much of science and mathematics, was developed partly as a result of people
recognizing and describing patterns. Today, we will observe, notice, and describe patterns; then we
will make predictions based
on what we discovered.
Example 1: Describe the pattern, then predict and sketch the next figure in the sequence.
Example 2: Describe the pattern in the numbers 1, 5, 9, 13,….Write the next three numbers in the
pattern.
The next three numbers are _______________________.
Checkpoint:
1. Sketch the next figure in each pattern.
2. Describe the pattern in the numbers 2, 8, 32, 128,…
and write the next three numbers in the pattern.
*Your description of the pattern you observed in each sequence is called a ____________.
CONJECTURE:
Example 3: Complete each conjecture and test it using several examples.
a. The sum of any three odd integers is _____________________.
b. The product of any two odd numbers is ____________________.
Section 2.1 Use Inductive Reasoning
Example 4: Make and test a conjecture about the product of any two odd integers.
Conjecture:
Looking for patterns and making conjectures is part of a process called _________________________.
A conjecture is ____________ if ______________________________________________________.
A conjecture is ____________ if ______________________________________________________.
COUNTEREXAMPLE:
Example 5: A student makes the following conjecture about the difference of two numbers. Find a
counterexample to disprove the student’s conjecture.
Conjecture: The difference of any two numbers is always smaller than the larger number.
Checkpoint
3. Find a counterexample to show that the following conjectures are false.
a. Conjecture: The quotient of two numbers is always smaller than the dividend.
b. Conjecture: All shapes with four sides the same length are squares.