Lesson 2 1 Inductive Reasoning EXAMPLE 1 Patterns

Lesson 2 -1: Inductive Reasoning

EXAMPLE 1 Patterns and Conjecture A. Write a conjecture that describes the pattern 2, 7, 12, 17, 22. Then use your conjecture to find the next item in the sequence. Step 1 Step 2 Look for a pattern. 2 7 12 Make a conjecture 17 22

EXAMPLE 2 Patterns and Conjecture A. Write a conjecture that describes the pattern 2, 4, 12, 48, 240. Then use your conjecture to find the next item in the sequence. Step 1 Step 2 Look for a pattern. 2 4 12 Make a conjecture 48 240

EXAMPLE 5 Patterns and Conjecture Write a conjecture that describes the pattern shown. Then use your conjecture to find the next item in the sequence.

EXAMPLE 6 Patterns and Conjecture Write a conjecture that describes the pattern shown. Then use your conjecture to find the next item in the sequence.

EXAMPLE 7 Algebraic and Geometric Conjectures A. Make a conjecture about the sum of an odd number and an even number. List some examples that support your conjecture. Step 1 List some examples. Step 2 Look for a pattern. Step 3 Make a conjecture.

• counterexample = false example to a conjecture • Number, drawing or statement

EXAMPLE 8 Find Counterexamples A: If <A and <B are complementary angles, then they share a common side. B: If a line intersects a segment at its midpoint, then the line is perpendicular to the segment. C: The sum of two numbers is always grater than the larger number