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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

For points pattern.L, M, and N, LM = 20, MN = 6, and LN = 14. Make a conjecture and draw a figure to illustrate your conjecture.

Counterexample pattern.

Counterexample pattern.

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

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

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

Given: x is an integer.

Conjecture: -x is negative.

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

Given: WXYZ is a rectangle.

Conjecture: WX = YZ and WZ = XY

Assignment: pattern.Pgs. 64 - 66 12-36 evens, 46-66 evens

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