Geometry Unit 2

Conjecture

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

Contrapositive

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

Valid argument

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

Geometric proof

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.

Conditional

A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a _____ statement.

Algebraic

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

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

Symmetric Property of Congruence

Conjunction

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

Argument

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

Proof

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 _____.

Formal

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.

No, 60 cannot be evenly divided by 7, 8, or 9.

Conjecture: The number 60 can be evenly divided by all numbers from 1 to 9. Is this conjecture true?

Yes.

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

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

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. is a ray.Conclusion:AB→ starts at one point and extends forever in one direction.

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 of Syllogism.

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.

Linear Pair

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

Hypothesis

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

Conclusion

The part of the conditional statement that expresses the action that will result if the conditions of the statement are met is called the _____.

Inductive

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.

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 and b=c

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

If a≠b or b≠c, then a≠c

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

The same expression is added to both sides of an equation if, and only if, both sides of the equation remain equal.

Which is a proper biconditional statement formed from the statement:

Distributive Property of Equality

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

Commutative Property of Multiplication

Which property is illustrated? xy=yx

Reflexive Property of Congruence

Which property is illustrated? ∠ABC≅∠ABC

Multiplication Property of Equality

Which property is illustrated? If x=2, then xy=2y

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.