Geometry U2 Practice Test

Which property is illustrated? xy=yx

Commutative Property of Multiplication

A _____ is a compound logic statement made up of two statements joined together with the word "and."

conjunction

A _____ is a related conditional statement that results from the exchange and negation of the hypothesis and conclusion of a conditional statement.

contrapositive

Which property is illustrated? If AB¯≅BC¯, then BC¯≅AB¯

Symmetric Property of Congruence

A(n) _____ proof is a proof that uses algebraic properties to reach a conclusion about an algebraic equation.

algebraic

A series of reasons that leads to a conclusion is an _____.

argument

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 _____ statement.

conditional

A(n) _____ is a statement that you conclude to be true based on logical reasoning.

conjecture

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 _____ is the part of a conditional statement that expresses the conditions that must be met.

hypothesis

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

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

valid argument

Which property is illustrated? 5(a+b)=5a+5b

Distributive Property of Equality

What is the converse of: If a=b and b=c , then a=c

If a=c, then a=b and b=c

What is the inverse of: If a=b and b=c , then a=c

If a≠b or b≠c, then a≠c

What is the contrapositive of: If a=b and b=c , then a=c

If a≠c then a≠b or b≠c

The _____ Theorem states that "If any two angles form a linear pair, then they are supplementary."

Linear Pair

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 cannot be evenly divided by 7, 8, or 9.

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.

Conjecture: When one plane intersects another plane, the intersection of the two planes is a line. Is this conjecture true?

Yes.

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 of Detachment.

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 it is autumn, the leaves will fall off the trees. If the leaves fall off the trees, I will have to pick up leaves. Conclusion: If it is autumn, I will have to pick up leaves.

Yes. This argument uses the Law of Syllogism.