1. Lesson 1-1 Patterns and Inductive Reasoning
Applied Geometry
Lesson 1-1
Patterns and Inductive Reasoning
Objective:
Learn and identify patterns and use inductive reasoning.

2. Inductive Reasoning
- method used to make a conclusion based on a pattern of examples or past events
Find the next three terms of the sequence
33, 39, 45 …
1, 3, 7, 13, 21…
51, 57, 63
+ 6
+ 6
31, 43, 57 +6
+10
+14 +2 +8
+12 +4

3. Your Turn Find the next 3 terms
1.25, 1.45, 1.65,…
13, 8, 3,…
1, 3, 9, …
32, 16, 8,…
10, 12, 15, 19…
1, 2, 6, 24…
+0.2 each time
/ 2 each time
1.85, 2.05, 2.25
4, 2, 1
-5 each time
+2, + 3, + 4
24, 30, 37
-2, -7, -12
*3 each time
*2, *3, *4
27, 81, 243
120, 720, 5040

4. Geometric Pattern
Draw the next figure in the pattern:
Next figure:

5. Example
Draw the next figure in the pattern.
The next figure

6. Your turn
Draw the next figure
The next figure:

7. Conjecture
A conjecture is a conclusion that you reach based on inductive reasoning.

8. The diagonals of a rectangle have the
Hands-on Activity
Draw 3 rectangles of different sizes
Draw the diagonals of all the rectangles.
Get a ruler and measure both diagonals of all 3 rectangles.
What is your conjecture about the diagonals of a rectangle?
The diagonals of a rectangle have the
same measure

9. Counterexample
Counterexample is an example that shows that a conjecture is false or not true.

10. Example Sample answer: ½ and 10 Said positive didn’t say had
Akira studied the data in the table and made the following conjecture.
The product of 2 positive numbers is always greater than either factor.
Factors
Product 2 8 16 5 15 75 20 38
760 54 62
3348
Find a counterexample for the
conjecture.
Sample answer: ½ and 10
Said positive didn’t say had
to be a whole number

11. Example
Provide a counterexample for the following conjecture:
Multiplying a number by –1 produces a product that is less than –1.
Sample answer:
(-1)(-2) = 2 which is greater than –1

12. Real World example 2005 – 10.9 billion dollars
The following graph shows the revenue from sale of waste management equipment in billions of dollars. Find a pattern in the graph and then make a conjecture about the revenue for 2005.
Increase of 0.2 billion
each year
2002 – 10.3 billion
2003 – 10.5 billion
2004 – 10.7 billion
2005 – 10.9 billion
dollars

13. Homework
Pg – 14 all, 16 – 38 Even