Geometry - U2
True or False: the act of forming conclusions based on available information is a conjecture.
False
Addition Property of Equality
For all expressions a , b , and c , if a=b , then a+c=b+c .
The _____ is the part of a conditional statement that expresses the conditions that must be met by the statement.
hypothesis
True or False: an example that proves a conjecture to be false is a counterexample.
true
A _____ is the degree of truth of a conditional statement.
truth value
conditional statement
a statement in which a conclusion is true if the conditions of a particular hypothesis are true
The exchange and negation of both the hypothesis and conclusion of a conditional statement results in a related conditional statement called a(n) _____.
contrapositive
The exchange of the hypothesis and conclusion of a conditional statement results in a related conditional statement called a(n) _____.
converse
A biconditional statement that is used to describe a geometric object or concept is called a _____.
definition
True or False: A biconditional statement is a statement in which a conclusion is true if the conditions of a particular hypothesis are true.
false
True or False: the process of reasoning that a rule, condition, definition, property, or statement is true because specific cases have been observed to be true is deductive reasoning.
false
The _____ is the negative form of any part of a conditional statement.
negation
True or False: A biconditional statement is a logical statement formed by the combination of a conditional statement and its converse.
true
inverse
The negation of the hypothesis and conclusion of a conditional statement results in a related conditional statement called a(n) _____.
True
True or False: A compound logic statement made up of two statements joined with the word "and" is a conjunction.
True
True or False: A series of reasons that leads to a conclusion is a valid argument.
False
True or False: An argument that uses logic in the form of definitions, properties, and previously proved principles to show that a conclusion is true is a valid argument.
True
True or False: The Associative Property of Addition states that for all expressions a, b, and c , (a+b)+c=a+(b+c) .
True
True or False: The Associative Property of Multiplication states that for all expressions a, b, and c. (ab)c = a(bc)
False
True or False: The Commutative Property of Addition states that for all expressions a and b, ab=ba
True
True or False: The Commutative Property of Multiplication states that for all expressions a and b, ab=ba
True
True or False:An application of deductive reasoning such that the reasoning is logically correct and undeniably true is a valid argument.
Transitive Property of Equality
Which property is illustrated? For all expressions a , b , and c , if a = b and b = c , then a = c .
Substitution Property of Equality
Which property is illustrated? For all expressions a and b , if a=b , then b can be substituted for a in any expression.
Symmetric Property of Equality
Which property is illustrated? For all expressions a and b , if a=b then b=a .
Transitive Property of Congruence
Which property is illustrated? If ΔA≅ΔB and ΔB≅ΔC, then
Multiplication Property of Equality
Which property is illustrated? x=y so
Reflexive Property of Congruence
Which property is illustrated? ∠A≅∠A
Associative Property of Multiplication
Which property is illustrated? (3x)y=3(xy)
Reflexitive
Which property of congruence is illustrated? For any geometric figure A , A≅A .
Transitive
Which property of congruence is illustrated? For any geometric figures A , B , and C , if A≅B and B≅C , then A≅C .
Symmetric
Which property of congruence is illustrated? For any geometric figures A and B , if A≅B , then B≅A .
Law of Detachment
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 Syllogism
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)
biconditional statement
a logical statement formed by the combination of a conditional statement and its converse
converse of a conditional statement
a related conditional statement in which the hypothesis and the conclusion of a conditional statement have been exchanged
contrapositive of a conditional statement
a related conditional statement resulting from the exchange and negation of both the hypothesis and conclusion of a conditional statement
inverse of a conditional statement
a related conditional statement resulting from the negation of the hypothesis and conclusion of a conditional statement
The part of a conditional statement that expresses the action that will result if the conditions of the statement are met is the _____.
conclusion
True or False: a statement concluded to be true based on logical reasoning is a conjecture.
true