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29 terms

Geometry Chapter 2 terms, postulates and theorems

Parker Glencoe
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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.