Lesson 2-1 Inductive Reasoning and Conjecture. Ohio Content Standards:

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Inductive Reasoning and Conjecture

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

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

Assignment: Pgs evens, evens