Geometry Chapter 2 terms, postulates and theorems

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Parker Glencoe

Conclusion

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

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.

Conjecture

An educated guess.

Contrapositive

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

Converse

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

Counterexample

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

Hypothesis

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

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.

Inverse

The denial of a statement.

Law of Detachment

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

Law of Syllogism

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

Deductive Reasoning

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

If - Then Statement

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

Negation

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

Proof

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

Two Column Proof

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

Venn Diagram

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

Addition and Subtraction Properties

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

Distributive property

a(b + c) = ab + ac

Multiplication and Division Properties

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

Reflexive Property

a=a

Substitution Property

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

Symmetric Property

if a=b, then b=a

Transitive Property

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

Segment Addition Postulate

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

Supplement Theorem

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

Linear Pair

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

congruent segments

Segments that have the same length

vertical angles

A pair of opposite congruent angles formed by intersecting lines.

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