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