Definitions

© 2006 by Mr. Mayers

ReasoningConditional Statements Properties

Undefined Terms Symmetry

Team 1 Team 2 Team 3 Team 4

0 0 0 0

What is the difference between an axiom and

a theorem?

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Axiom-statement accepted as fact

Theorem-statement proven based on fact

What type of reasoning is used?

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Inductive Reasoning

Every Wednesday we have a checklist in Geometry. It’s Wednesday. We are going to have a checklist.

Identify the hypothesis:If I graduate from Simon Tech, then I go to college.

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I graduate from Simon Tech

What property says A=A?

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Reflexive

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Answers may vary.

Name four points that are coplanar.

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Name what type(s) of symmetry.

Reflectional (2 lines of symmetry) and Rotational (2-fold)

What is reflectional symmetry?

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When one shape becomes congruent to another when

you flip it along a line of symmetry

Use inductive reasoning to find what comes next in the sequence 0, 2, 5, 9, 14, _______, _______

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20, 27

Write the following statement in “if-then”

form.“Every Simon Tech

student goes to college.”

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If you’re a Simon Tech student, then you go to college.

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Which of the following is a counterexample to this statement: If you live in Los Angeles, then you live in Lynwood. A. Someone who lives in ComptonB. Someone who lives in New York CityC. Someone who lives in TexasD. Someone who lives in San Francisco

A

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RT or RQ or TQ or h

Name a line that contains points R and T.

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Name what type(s) of symmetry.

Rotational (4-fold)

What is the difference between a conditional statement and its contrapositive?

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Same validity, but conditional is If P then Q, contrapositive is If not Q then not P.

What can we conclude using deductive reasoning.

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Andrea studied.

If Andrea does not study for the test, she will not pass. Andrea passed the test.

Write the inverse.“If you like chocolate,

then you like cheesecake.”

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If you don’t like chocolate then you

don’t like cheesecake.

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Which property is used? Mike is taller than Angela. Mario is taller than Mike. Therefore,

Mario is taller than Angela.

Transitive Property

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Name a ray that starts at the intersection and continues left

MA or MC

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Name what type(s) of symmetry

None

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Prove a statement false,

Fit the hypothesis but not the conclusion.

What does a counterexample have to do?

What type of reasoning is used?

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Deductive reasoning.

If it rains, we will stay inside. If we stay inside, we will make pizza. It is raining. Therefore, we will make pizza.

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If it’s a rectangle then it’s a square.

Write the converse:If it’s a square, then it’s a

rectangle.

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What is another name for the Transitive Property?

Law of Syllogism

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How many planes contain the point L?

3

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Name what type(s) of symmetry.

Rotational (2-fold)

Name the law: If a conditional statement is true and its hypothesis is true, then its conclusion is true.

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Law of Detachment

What other statement must be true if the following statement is true? “If it is Friday, we will have an auction.”

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If we don’t have an auction, it is not Friday.

Which statement always has the same truth value as the converse?

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Inverse

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If a=b, then b=a.

In logic, if P Q (conditional), then Q P (converse). Together, biconditional

Describe the Symmetric Property.

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Name a point that is collinear to point N.

P or R or M

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Write a statement that your whole group is a counterexample to.