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