Geometry

  1. Logic and Geometric Proofs
    1. Types of Reasoning
      1. Inductive Reasoning
        1. Making Conjectures from Patterns
          1. Limitations of Inductive Reasoning
            1. Counterexamples
            2. Deductive Reasoning
              1. Logical Arguments
                1. Valid vs Invalid Arguments
                  1. Laws of Logic
                    1. Law of Detachment
                      1. Law of Syllogism
                  2. Conditional Statements
                    1. If-Then Statements
                      1. Hypothesis and Conclusion
                        1. Truth Value of Conditionals
                        2. Converse
                          1. Definition and Formation
                            1. Truth Value of Converse
                            2. Inverse
                              1. Definition and Formation
                                1. Truth Value of Inverse
                                2. Contrapositive
                                  1. Definition and Formation
                                    1. Truth Value of Contrapositive
                                    2. Logically Equivalent Statements
                                    3. Biconditional Statements
                                      1. Definition and Notation
                                        1. When to Use Biconditionals
                                          1. Writing Biconditional Statements
                                            1. Truth Conditions for Biconditionals
                                            2. Properties of Equality
                                              1. Reflexive Property
                                                1. Symmetric Property
                                                  1. Transitive Property
                                                    1. Substitution Property
                                                      1. Addition Property
                                                        1. Subtraction Property
                                                          1. Multiplication Property
                                                            1. Division Property
                                                            2. Properties of Congruence
                                                              1. Reflexive Property of Congruence
                                                                1. Symmetric Property of Congruence
                                                                  1. Transitive Property of Congruence
                                                                  2. Writing Geometric Proofs
                                                                    1. Structure of a Proof
                                                                      1. Given Information
                                                                        1. Prove Statement
                                                                          1. Statements and Reasons
                                                                          2. Two-Column Proofs
                                                                            1. Format and Organization
                                                                              1. Writing Effective Two-Column Proofs
                                                                              2. Flowchart Proofs
                                                                                1. Structure and Symbols
                                                                                  1. Creating Flowchart Proofs
                                                                                  2. Paragraph Proofs
                                                                                    1. Writing Style and Organization
                                                                                      1. Transitional Phrases
                                                                                      2. Common Proof Strategies
                                                                                        1. Working Backwards
                                                                                          1. Auxiliary Lines
                                                                                            1. Proof by Cases
                                                                                            2. Justifying Statements in Proofs
                                                                                              1. Using Definitions
                                                                                                1. Using Postulates
                                                                                                  1. Using Theorems
                                                                                                    1. Using Given Information

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                                                                                                3. Parallel and Perpendicular Lines

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                                                                                                5. Triangles