2.1 Inductive Reasoning
Describe how to sketch the fourth figure in the pattern.
Then, sketch the fourth and fifth figure.
Figure 1
Figure 2
Figure 3
2.1 Inductive Reasoning
2.1 Use Inductive Reasoning
Describe the pattern in the numbers and write the
next three numbers.
a) 51, 17, 17/3, 17/9,...
17/27, 17/81, 17/243
÷3
b) –7, –28, –112, –448,...
-1792, -7168, -28672
*4
Ex 1 Sketch the next figure.
1
2.1 Inductive Reasoning
A conjecture
an unproven statement that is based on
ovservations
Inductive Reasoning:
1. Look for a pattern.
2. Make a conjecture
3. Verify the conjecture.
Example: Given five collinear points, make a conjecture about
the number of ways to connect different pairs of the
points.
Example: Numbers such as 3, 4, and 5 are called consecutive
integers. Make and test a conjecture about the sum of any
three consecutive integers.
0+1+2 = 3
2+3+4 = 9
6+7+8 = 21
10+11+12 = 33
11+12+13 = 36
2
Conjecture: Multiply the middle number by 3.
2.1 Inductive Reasoning
Disproving Conjectures
counterexample -
any example for which the conjecture is
false.
Example: Find a counterexample to disprove the student's
conjecture below.
Conjecture: The difference of 2 positive numbers is always
positive.
Counterexample: 4 - 11 = -7
Guided practice:
Find a counterexample to show that the following conjecture
is false.
The value of x2 is always greater than the value of x.
Homework:
Pages 75-78 # 3-5, 7-19 odd, 20, 21, 22-28 even, 32-36
2.1 Inductive Reasoning
1. Describe a pattern in the numbers. Write the next three
numbers in the pattern. 20, 22, 25, 29, 34,...
2. Find a counterexample for the following conjecture: If the
sum of two numbers is positive, then the two numbers must be
positive.
3. Find the complement and supplement of XYZ if
m XYZ = 80º.
4. Find the values for y in the following figure.
(4y– 7)º
(5y–2)º