GEOMETRY 10-12



Notes: Geometry Ch. 2 Reasoning and Proof Name___________________

2-1: Use Inductive Reasoning

conjecture:

inductive reasoning:

counterexample:

2-2: Analyze Conditional Statements

conditional statement:

converse:

inverse:

contrapositive:

biconditional statement

perpendicular lines

2-3: Apply Deductive Reasoning

deductive reasoning:

Laws of Logic:

1. Law of Detachment (direct argument)

2. Law of Syllogism (chain rule)

2-4: Use Postulates and Diagrams

Point, Line, and Plane Postulates:

1. Postulate 5: Through any ____ points there exists exactly ____ line.

2. Postulate 6: A line contains at least ____ points.

3. Postulate 7: If ____ lines intersect, then their intersection is exactly ____ point.

4. Postulate 8: Through any ____ noncollinear points there exists exactly ____ plane.

5. Postulate 9: A plane contains at least ____ noncollinear points.

6. Postulate 10: If ____points lie in a plane, then the line containing them lies in the ______.

7. Postulate 11: If ____ planes intersect, then their intersection is a _______.

line perpendicular to a plane:

2-5: Reason Using Properties from Algebra

Algebraic Properties of Equality:

Addition Property:

Subtraction Property:

Multiplication Property:

Division Property:

Substitution Property:

Other Properties of Equality:

Reflexive Property:

Symmetric Property:

Transitive Property:

2-6: Prove Statements about Segments and Angles

proof: theorem:

Two-column Proof:

2-7: Prove Angle Pair Relationships

1. Congruent Supplements Theorem

2. Congruent Complements Theorem

3. Linear Pairs Postulate:

4. Vertical Angles Postulate:

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