GEOM U2
A ____ is a compound logic statement made up of two statements joined together with the word "and"
conjunction
A _____ is an application of deductive reasoning such that the reasoning is logically correct and undeniably true.
valid argument
A _____ is a related conditional statement that results from the exchange and negation of the hypothesis and conclusion of a conditional statement.
contrapositive
The _____ is the part of a conditional statement that expresses the conditions that must be met.
hypothesis
Which property is illustrated? If AB¯≅BC¯, then BC¯≅AB¯
Symmetric Property of Congruence
An argument that uses logic in the form of definitions, properties, and previously proved principles to show that a conclusion is true is called a _____.
proof
A series of reasons that leads to a conclusion is an ___
arguement
Which property is illustrated? xy=yx
Commutative Property of Multiplication
What is the contrapositive of: If a=b and b=c , then a=c
If a≠b or b≠c, then a≠ c
a law of deductive reasoning that states that if a conditional statement is true and its hypothesis is true, then its conclusion will also be true; [(p→q)∧p]→q
Law of Detachment
a law of deductive reasoning that states that if two conditional statements are true, and if the conclusion of the first statement is the hypothesis of the second statement, then a conclusion based on the conditional statements will also be true; [(p→q)∧(q→r)]→(p→r)
Law of Syllogism
Which property is illustrated? If x=2, then xy=2y
Multiplication Property of equality
Conjecture: The number 60 can be evenly divided by all numbers from 1 to 9. Is this conjecture true?
No, 60 can also be evenly divided by 15, 20, and 30
Is this a valid argument? Given: If a geometric figure starts at a point and extends forever in one direction, then it is a ray. AB→ is a ray. Conclusion:AB→ starts at one point and extends forever in one direction.
No. This is an improper use of the Law of Detachment
Which property is illustrated? ∠ABC≅∠ABC
Reflexive Property of Congruence
Which is a proper biconditional statement formed from the statement: If the same expression is added to both sides of an equation, then both sides of the equation remain equal.
The same expression is added to both sides of an equation if, and only if, both sides of the equation remain equal.
Is this a valid argument? Given: If it is July 4th, then we celebrate Independence Day. Today is July 4th. Conclusion: Today, we celebrate Independence Day.
Yes. This argument uses the Law of Detachment
Is this a valid argument? Given: If an object is in the shape of a sphere, then it rolls. This ball is in the shape of a sphere. Conclusion: This ball rolls.
Yes. This argument uses the law detachment
an ____ proof is a proof that uses algebraic properties to reach a conclusion about an algebraic equation
algebraic
The part of the conditional statement that expresses the action that will result if the conditions of the statement are met is called the _____.
conclusion
A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a ___
conditional
A ___ is a statement that you conclude to be true based on logical reasoning
conjecture
Which property is illustrated? 5(a+b)=5a+5b
distributive property of equality
What is the inverse of: If a=b and b=c , then a=c
f a≠b or b≠c, then a≠c
An argument that uses written justification in the form of definitions, properties, and previously proved geometric principles to show that a conclusion is true is called a _____ proof.
formal
A ___ is an argument that uses written justification in the form of definitions, properties, postulates, and previously proved theorems and corollaries to show that a conclusion is true
geometric proof
The process of reasoning that a rule, condition, definition, property, or statement is true because specific cases have been observed to be true is called _____ reasoning.
inductive
The ___ Theorem states that "if any two angles form a linear pair, then they are supplementary"
linear pair