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Conclusion

In a conditional statement, the statement that immediately follows the word then.

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Conditional Statement

A statement of the form "If A, then B." The part following if is called the hypothesis. The part following then is called the conclusion.

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Conjecture

An educated guess.

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Contrapositive

The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

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Converse

The statement formed by interchanging the hypothesis and the conclusion of a conditional statement.

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Counterexample

An example used to show that a given general statement is not always true.

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Hypothesis

In a conditional statement, the statement that immediately follows the word if.

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Inductive reasoning

Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction. Conclusions arrived at by inductive reasoning lack the logical certainty of those arrived at by deductive reasoning.

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Inverse

The denial of a statement.

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Law of Detachment

If p-->q is a true conditional and p is true, then q is true.

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Law of Syllogism

If p-->q and q-->r are true conditionals, then p-->r is also true.

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Deductive Reasoning

reasoning used to reach conclusions that must be true wherever the assumptions on which the reasoning is based are true

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If - Then Statement

a compound statement of the form "If A, then B," where A and B are statements

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Negation

to deny a statement is to negate a statement, (logic) a proposition that is true if and only if another proposition is false

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Proof

a formal series of statements showing that if one thing is true something else necessarily follows from it

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Two Column Proof

a type of proof written as numbered statements and reasons that show the logical order of an argument

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Venn Diagram

A diagram that uses circles to display elements of different sets. Overlapping circles show common elements.

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Addition and Subtraction Properties

If a = b, then a + c = b + c

If a = b, then a - c = b - c

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Distributive property

a(b + c) = ab + ac

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Multiplication and Division Properties

for all numbers a, b, and c if a=b then a**c=b**c and if c does not equal 0 then a/c=b/c

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Substitution Property

If a=b, then a can be substituted for b in any equation or expression

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Symmetric Property

if a=b, then b=a

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Transitive Property

If a=b and b=c, then a=c

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Segment Addition Postulate

If B is between A and C, then AB+BC=AC

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Supplement Theorem

If two angles form a linear pair, then they are supplementary angles,, Supplements of congruent angles are congruent

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Linear Pair

a pair of adjacent angles whose non-common sides are opposite rays

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congruent segments

Segments that have the same length

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vertical angles

A pair of opposite congruent angles formed by intersecting lines.

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