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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:


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


Conjecture

  • An educated guess based on known information


Inductive Reasoning


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.


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


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.


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. 64 - 66 12-36 evens, 46-66 evens


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