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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