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30 Cards in this Set
- Front
- Back
- 3rd side (hint)
conjecture
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unproven statement that is based on observations
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counterexample
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a specific case for which the conjecture is false
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conditional statement
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a logical statement that has a hypothesis and conclusion. written in if-then form
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if p, then q
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converse
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exchange the hypothesis and conlusion.
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if q, then p
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inverse
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negate the hypothesis and conlusion
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if not p, then not q
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contrapositive
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first write the converse, then negate the conclusion and hypothesis
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if not q, then not p
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perpendicular lines
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if two lines intersect to form a right angle, then they are perpendicular lines
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biconditional statement
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contains the phrase if and only if. when converse and conditional are both true
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p if and only if q
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inductive reasoning
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uses specific examples and patterns to form a conjecture
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deductive reasoning
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uses facts, definitions, accepted properties and the laws of logic to form a logical statement
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law of detachment
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if the hypothesis of a conditional statement is true, then the conclusion is also true
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law of syllogism
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p>q, q>r, then p>r
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line perpendicular to a plane
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a line is a line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point
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ruler postulate
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the distance between points A and B written as AB is the absolute value of the difference of the coordinates of A and B
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segment addition postulate
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if B is between A and C then AB +BC =AC
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angle addition postulate
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if P is in the interior of <RST, then the measure of <RST is equal to the sum of the measures of <RSP and <PST.
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if p is in the interior of < RST, then m<RST =m<RSP + m<PST
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addition property
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if a =b, then a+c =b+c
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subtraction property
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if a=b, then a-c=b-c
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multiplacation property
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if a=b, then ac=bc
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division property
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if a=b and c doesnt = 0, then a÷c=b÷c
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substitution property
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if a=b, then a can be substituted for b in any equation or expression
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reflexive property
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for any real number a, a=a
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symmetric property
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for any real numbers a and b, if a=b, then b=a
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transitive property
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for any real numbers a,b, and c, if a=b and b=c, then a=c
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right angle congruence theorem
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all right angles are congruent. rt <'s =~ thrm.
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congruent supplements theorem
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if two angles are supplementary to the same angle or congruent angles, then they are congruent.
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congruent complements theorem
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if two angles are complementary to the same angle or congruent angles, then they are congruent
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linear pair postulate
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if two angles form a linear pair, then they are supplementary.
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vertical angles congruence theorem
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vertical angles are congruent
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right angle congruence theorem
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all right angles are congruent. rt <'s =~ thrm.
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