Geometry – Lesson 1.1
Patterns and Inductive Reasoning
Geometry 1.1
You may take notes on your own
notebook or the syllabus and notes
packet.
 Make sure that you keep track of your
vocabulary. One of the most challenging
aspects of geometry compared to other
math classes is the vocabulary!

Geometry 1.1 - Notes

Sketch the next figure (4) in the following
pattern.
Geometry 1.1 - Notes

Sketch the next figure (5) in the following
pattern.
Geometry 1.1 - Notes

Describe the “pattern” in words.
How would you tell a friend how to draw
this pattern?
Geometry 1.1 – Vocabulary
Conjecture:
A conjecture is an unproven
statement that is based on
observations.
Geometry 1.1 – Vocabulary
Inductive Reasoning:
The process of looking for a
pattern, making a conjecture,
and verifying the conjecture is
true.
Geometry 1.1 – Notes
How do you prove a conjecture is true?
We must demonstrate or
prove that the statement is
true for EVERY case.
Geometry 1.1 – Notes
How do you prove a conjecture is false?
We must find one example
which makes the conjecture
false.
Geometry 1.1 – Vocabulary
Counterexample:
A counterexample is an
example which shows the
conjecture is false.
Geometry 1.1 – Notes
Make a conjecture for the following pattern.
Geometry 1.1 – Notes
Patterns may also exist in a sequence of numbers.
Can you find a conjecture for each pattern?
3, 6, 12, 24, …
20, 15, 10, 5, …
2, 3, 5, 8, 12 …
Geometry 1.1 – Notes
Can you find a counterexample for each conjecture?
Squaring a whole number and
adding one will always be an
even number.
For any number x, x2 is
always larger than x.
Geometry 1.1 – Notes
Check for understanding:
Write a conjecture for the TOTAL number of objects
in each diagram.
Geometry 1.1 – Homework
You now have time to start on homework. It is listed
on the Chapter 1 Notes Sheet