# Lesson 2-1 - PowerPoint PPT Presentation

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Lesson 2-1. Inductive Reasoning and Conjecture. Ohio Content Standards:. Ohio Content Standards:. Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

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Lesson 2-1

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## Lesson 2-1

Inductive Reasoning and Conjecture

### Ohio Content Standards:

• Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

### Ohio Content Standards:

• Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

### Ohio Content Standards:

• Generalize and explain patterns and sequences in order to find the next term and the nth term.

### Conjecture

• An educated guess based on known information

### Inductive Reasoning

• Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction

### Make a conjecture about the next number based on the pattern.

2, 4, 12, 48, 240

### Counterexample

• A false example to show that a conjecture is not true

### Determine whether each conjecture is true or false. Give a counterexample for any false conjecture.

Given: x is an integer.

Conjecture: -x is negative.

### Determine whether each conjecture is true or false. Give a counterexample for any false conjecture.

Given: WXYZ is a rectangle.

Conjecture: WX = YZ and WZ = XY