Chapter 2 by Jazmine Lineberger

Inductive Reasoning

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Reasoning based on patterns you observe

Conjecture

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A conclusion reached using inductive reasoning

Counterexample

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An example that proves a conjecture wrong

Conditional

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An if-then statement

Hypothesis

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A proposition made as a basis of reasoning (the if statement in a conditional)

Conclusion

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A judgement or decision reached by reasoning ( the then statement in a conditional)

Truth Value

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Whether a conditional is true or false

Converse

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Exchange the hypothesis and the conclusion

Inverse

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Negate both the hypothesis and the conclusion of the conditional

Contrapositive

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Negate both the hypothesis and the conclusion of the converse

Equivalent Statement

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Statements with the same truth value

Biconditional

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A single true statement that combines a true conditional and its true converse

Deducvtive Reasoning

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Process of reasoning logically from given statements or facts to a conclusion

Law of Detachment

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If the hypothesis is true, then the conclusion is true

Law of Syllogism

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Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of another statement

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Proof

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A convincing argument that uses deductive reasoning. A proof logically shows why a conjecture is true.

Two-Column Proof

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Lists each statement on the left and the justification for it on the right

Vertical Angles Theorem

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Vertical angles are congruent

Congruent Supplements Theorem

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If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent

Congruent Complements Theorem

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If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent

Theorem 2-4

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All right angles are conguent

Theorem 2-6

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If two angles are congruent and supplementary, then each is a right angle

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Inductive Reasonin

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The next triangle will have 21 dots

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Conjecture: When you multiply a number by 3, the product is divisible by 6
Counter example: 3 * 3 = 9 and 6 doesn't divide into 9 evenly

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Statement Example Truth Value
Conditional If mConverse If m Inverse If mContrapositive If m

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