Download Geometry B Date: ______ 2.1 Using Inductive Reasoning to Make

Geometry B
Date: ____________
2.1 Using Inductive Reasoning to Make Conjectures
Objective: To use inductive reasoning to identify patterns and make conjectures
To find counterexamples to disprove conjectures
Definitions:

Inductive Reasoning - _____________________________________________________

Conjecture - _____________________________________________________________
Ex. 1: Identifying a Patterns
Find the next item in each pattern.
a. Monday, Wednesday, Friday, ...
b. 3, 6, 9, 12, 15,…
c.  ,  ,  , …
Ex. 2: Making a Conjecture
Complete each conjecture. List some examples or draw a picture to look for patterns.
a. The product of an even number and an odd number is _________.
b. The number of segments formed by n collinear points is ______________________________.
Practice:
a. The sum of two positive numbers is _______________.
b. The product of any two odd numbers is _________________.
Ex. 3: Biology Application
To learn about the migration behavior of California gray whales, biologist observed whales along
two routes. For seven days, they counted the number of whales seen along each route. Make a
conjecture based on the data.
Conjectures:
 To show a conjecture is always true, _________________________

To show a conjecture is false, _______________________________________________
o This is called a _________________________, and can include:
 Drawings
 Statements
 Numbers
Ex. 4: Finding a Counterexample
Show that each conjecture is false by finding a counterexample.
a. For every integer n, n 3 is positive.
b. Two complementary angles are not congruent.
Practice:
a.. Supplementary angles are adjacent.
b. For any real number x, x 2  x .
HW: Worksheet 2.1