Geometry Unit 2

the part of a conditional statement that expresses the action that will result if the conditions of the statement are met

conclusion

the part of a conditional statement that expresses the conditions that must be met by the statement

hypothesis

Which property is illustrated? For all expressions a , b , and c , if a=b , then a+c=b+c .

Addition Property of Equality

Which statement is a proper biconditional statement formed from the conditional statement: If an angle is bisected, then it is divided into two congruent angles.

An angle is bisected if, and only if, it is divided into two congruent angles.

Which property is illustrated? (3x)y=3(xy)

Associative Property of Multiplication

Which statement is the converse of the conditional statement: If two figures have the same shape and size, then they are congruent.

If two figures are congruent, then they have the same shape and size.

Which statement is the contrapositive of the conditional statement: If two figures have the same shape and size, then they are congruent.

If two figures are not congruent, then they do not have the same shape and size.

What statement is the inverse of the conditional statement: If two figures have the same shape and size, then they are congruent.

If two figures do not have the same shape and size, then they are not congruent.

a proof that uses algebraic properties to reach a conclusion about an algebraic equation

algebraic proof

a universally accepted statement about an algebraic expression or equation that holds true in every instance in which the conditions of the property are met

algebraic property

a related conditional statement resulting from the exchange and negation of both the hypothesis and conclusion of a conditional statement

contrapositive of a conditional statement

a related conditional statement in which the hypothesis and the conclusion of a conditional statement have been exchanged

converse of a conditional statement

a biconditional statement that is used to describe a geometric object or concept

definition

a number, symbol, or group of numbers and/or symbols with their operations used to express some mathematical fact, quantity, or value

expression

an argument that uses written justification in the form of definitions, properties, and previously proved geometric principles to show that a conclusion is true

formal proof

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

a property that compares the congruence of one geometric figure with the same or another geometric figure

geometric property

the process of reasoning that a rule, condition, definition, property, or statement is true because specific cases have been observed to be true

inductive reasoning

an argument that uses logic without written justification to show that a conclusion is true

informal proof

inverse of a conditional statement related conditional statement resulting from the negation of the hypothesis and conclusion of a conditional statement

inverse of a conditional statement

the statement of the reason for each step in a proof

justification

the negative form of any part of a conditional statement

negation

an argument that uses logic in the form of definitions, properties, and previously proved principles to show that a conclusion is true

proof

the act of forming conclusions based on available information

reasoning

the converse, inverse, and contrapositive of a conditional statement

related conditional statements

an example that proves a conjecture false

counterexample

the degree of truth of a conditional statement

truth value

an application of deductive reasoning such that the reasoning is logically correct and undeniably true

valid argument

Choose the correct number to continue the pattern: 0, 5, 2, 7, 4, 9, 6, _____

11

Choose the correct number to continue the pattern: 1, 3, 5, 7, 9, 11, _____

13

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? x=y so 4x=4y

Multiplication Property of Equality

Is this a valid argument? Given: If a flame is applied to paper, then the paper will burn. If there are ashes, then the paper burned. Conclusion: A flame burned the paper to ashes.

No. This is an improper use of the Law of Syllogism.

Which property of congruence is illustrated? For any geometric figure A , A≅A .

Reflexive

Which property is illustrated? ∠A≅∠A

Reflexive Property of Congruence

Which property is illustrated? For all expressions a and b , if a=b , then b can be substituted for a in any expression.

Substitution Property of Equality

Which property of congruence is illustrated? For any geometric figures A and B , if A≅B , then B≅A .

Symmetric

Which property is illustrated? For all expressions a and b , if a=b then b=a .

Symmetric Property of Equality

Which property of congruence is illustrated? For any geometric figures A , B , and C , if A≅B and B≅C , then A≅C .

Transitive

Which property is illustrated? If ΔA≅ΔB and ΔB≅ΔC, then ΔA≅ΔC

Transitive Property of Congruence

Which property is illustrated? For all expressions a , b , and c , if a = b and b = c , then a = c .

Transitive Property of Equality

Which statement is a proper biconditional statement formed from the conditional statement: If today is Friday, then we will have pizza for lunch.

We will have pizza for lunch today if, and only if, today is Friday.

a compound logic statement made up of two statements joined together with the word "and"; p∧q

conjunction

Is this a valid argument? Given: If two points lie on the same plane, then they are coplanar. Points X and Y both lie on plane R. Conclusion: Points X and Y are coplanar.

Yes. This argument uses the Law of Detachment.

Is this a valid argument? Given: If the temperature is below 32∘F, then water will freeze. If water freezes, then it will turn into a solid. Conclusion: If the temperature is below 32∘F, water will turn into a solid.

Yes. This argument uses the Law of Syllogism.

a series of reasons that leads to a conclusion

argument

a logical statement formed by the combination of a conditional statement and its converse, and can be written as "if and only if"

biconditional statement

a statement in which a conclusion is true if the conditions of a particular hypothesis are true, and can be written in if-then form

conditional statement

angles that have the same measure

congruent angles

a statement concluded to be true based on logical reasoning

conjecture

a statement or conjecture that can be proven by undefined terms, definitions, postulates, and previously proven theorems

theorem