1. Patterns and Inductive Reasoning
Geometry – Lesson 2.1
Patterns and Inductive Reasoning

2. Geometry Notes
Sketch the next figure (4) in the following pattern.

3. Geometry Notes
Sketch the next figure (5) in the following pattern.

4. Geometry 2.1 - Notes Describe the “pattern” in words.
How would you tell a friend how to draw this pattern?

5. Geometry 2.1 - Notes Describe the “pattern” in words.
Must state two things: how to start, and how to get the next object from the previous
Ex: Start with one square. Add a new column to the left of the previous square with one more square than the previously added column

6. Geometry 2.1 – Vocabulary
Conjecture:
A conjecture is an unproven statement that is based on observations.

7. Geometry 2.1 – Vocabulary
Inductive Reasoning:
The process of looking for a pattern, making a conjecture, and verifying the conjecture is true.

8. Geometry 2.1 – Notes
How do you prove a conjecture is true?
We must demonstrate or prove that the statement is true for EVERY case.

9. Geometry 2.1 – Notes
How do you prove a conjecture is false?
We must find one example which makes the conjecture false.

10. Geometry 2.1 – Vocabulary
Counterexample:
A counterexample is an example which shows the conjecture is false.

11. Geometry 2.1 – Notes
Make a conjecture for the following pattern.

12. Geometry 2.1 – 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 …

13. Geometry 2.1 – 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.

14. Geometry 2.1 – Notes Check for understanding:
Write a conjecture for the TOTAL number of objects in each diagram.